In this paper we compared time-domain FWI problem vs. frequency-domain in terms of the behavior of cost function and model misfit error on a synthetic model with transmission geometry. Synthetic data was generated by solution of 2D acoustic wave equation and optimization was performed using L-BFGS algorithm for both approaches in time and frequency-domain. Although FWI problem has a better expression in frequency-domain but inversion of selected frequency components is drawback of this approach despite its lower computational costs in term of memory. This paper shows the difference of full band data inversion in the time-domain with sequential inversion of some selected frequency components in the frequency-domain numerically. According to the results timedomain FWI leads to better results due to its full band characteristics when computational resources permits us to use it.@en