Nuclear magnetic resonance (NMR) logging has become an important technique for formation evaluation, detecting interaction signals between H protons and applied magnetic fields. Measured decay signals called relaxation, contain important information about density of H protons and different decay rate due to its fluid type in the sensitive area. Thus, petrophysical information such as porosity, permeability and wettability can be estimated through the interpretation of the decay signals. Many researches on random walk simulation have been published, since a simulation method based on random walk for solving exponential decays was adapted in the early of 1950. This study first makes a review on NMR simulation researches, explains two most important methods: simulation with or without considering magnetic field gradient. Lastly, the study makes a comparison between NMR simulation responses with and without magnetic field gradient to show the importance to consider magnetic gradient to analyze the effects of magnetic gradients on NMR responses.