Suction caissons have been used extensively for anchoring and supporting the offshore installations like oil platforms and wind turbines. These foundations are normally subjected to complex combinations of the vertical, horizontal and moment loads (i.e. V, H, M) from the self-weight, wind, wave and currents. In the past decades, extensive studies have been conducted to investigate the combined V-H-M loading behaviour of suction caissons in clay. However, most existing studies are focused on the ultimate bearing capacity, while the deflection response is more critical in foundation design for recent infrastructures like offshore wind turbines. Due to the complex load conditions, predicting the three-dimensional (3D) deflection response of the foundation is still challenging. Machine learning (ML) appears on the research horizon due to its excellent capacity of solving nonlinear problems with desired speed and accuracy. However, conventional machine learning approaches were limited in their capacity to analyze raw natural data without artificial interventions. Meanwhile, the deep learning technique (DL), as a branch of machine learning, allows a machine to be fed with raw data, automatically extract the features, and discover intricate structures in high-dimensional data. The deep learning technique has been used in many fields like language translation, auto-pilot and image recognition. And Deep neural networks, including deep learning algorithms and architectures, are gradually being developed. In light of these backgrounds, this study proposed to develop a deep learning based surrogate model to predict the 3D deflection response of suction caissons under combined V-H-M loading. The advanced three-dimensional nonlinear finite element (FE) simulations under complex V-H-M loading paths were performed on suction caissons of different geometric configurations and in clay soils with different stiffness and strength properties. The 3D FE simulation data was then used to train the deep learning based design model. Three popular neural network structures, i.e., Feed forward Neural Network (FNN), Convolution Neural Network (CNN), Recurrent Neural Network (RNN) have been employed to develop the hybrid surrogate design model. In this study, two different training strategies were proposed for this geotechnical problem. In the first category, the 3D load-deflection behaviour of suction caisson is idealized as a point-to-point mapping problem, i.e. mapping between the deflections (i.e. displacement and rotation) with loads (i..e force and moment). This task was achieved by Fully-Connected Neural Network model (FC-NN) based on FNN, One Dimension Convolution Neural Network model (1D-CNN) based on CNN and Long Short Term Memory model (LSTM) based on RNN. In the second training strategy, the load-deflection response was idealized as a time series process, a line-to-line mapping problem, mapping between the past loading paths (i.e. 10 groups of forces and moments) with future loading paths (i.e. 90 groups of forces and moments). Besides the three neural network models mentioned before, another two complex and advanced models, LSTM Model combined with convolution neural network (1D-CNN+LSTM) and Temporal Convolutional Network model (TCN), are also applied for temporal prediction. The performance and training efficiency of these models were also systematically evaluated by interpolation and extrapolation experiments. Basically, all the models can well capture the 3D deflection response of the foundation with significantly high accuracy (i.e., root mean squared error is smaller than 0.05 and coefficient of determination is near 1.000) than the traditional design approach (such as macro-elements model), and with greater efficiency than the 3D FE simulations. Among all the models, the TCN model has the highest prediction accuracy and robustness. However, the FC-NN model has the simplest model structure and highest computational efficient in learning the non-linear relationship between deflection response and V-H-M load. Besides capturing the relationship between input and output, the deep learning model can also assist to identify the intrinsic failure mechanism. By observing the fluctuation of generalisation ability, the evolution of the failure mechanism of suction caisson with embedment depth was revealed.