The idea of capturing an asteroid has gained more and more attention in recent years, sparked by rapid technological development and the growing general interest into the subject, both by scientists and commercial parties. The focus of this thesis project lies on transferring a near-Earth asteroid (NEA) from its original orbit to a safe, stable and easily accessible location with respect to the Earth using low-thrust engines. It has been decided to aim for a final state in a heliocentric orbit, but in the vicinity of the Earth. By means of a selection process in which a constrained set of NEA’s were assessed for the required velocity impulse to transfer them to the Earth, the choice was made to use the asteroid 2006 RH120 for this research study. A stability analysis was performed, where fictional objects were placed in states that differed in two different Kepler elements with respect to the state of the Earth. These objects were subsequently propagated for 100 years and their behaviour during this time frame was analysed. It was found that by adding at least 0.03 to the eccentricity of the state of the Earth would result in a safe, stable and easily accessible orbit with respect to the Earth. The final phase of this study was to design the actual transfer trajectory from the asteroid’s initial orbit to this suitable state. A preliminary analytical analysis using the hodographic method was performed to obtain the most optimal combination of the departure date and time of flight, as well as creating a good initial guess for the upcoming numerical analysis. This was performed using Sims-Flanagan’s method, of which the originally implemented software in Tudat was modified to enable the inclusion of perturbing forces working on the asteroid throughout its trajectory, for increased realism. The results obtained by Sims-Flanagan’s method using several of the analysed initial guesses were around 1000 m/s for the required total velocity impulse and 1.75 N for the maximum thrust force. Due to the complexity of the problem, the use of Sims-Flanagan’s method and despite tuning of the algorithm, a small mismatch halfway the trajectory persisted, which caused the asteroid to not reach the exact most desired final state. It is therefore recommended to perform a better tuning of the algorithm to obtain a zero mismatch, with which the desired final state will be reached.