MR imaging pulse sequences can be made sensitive to motion by adding gradients with different strengths at different time intervals. In the well-known phase mapping method, such velocity encoding gradients are used to obtain phase information linear to the velocity of the studied object in the direction of the gradient. When very low velocities are studied, a long duration velocity-encoded gradient is required to obtain sufficient velocity sensitivity. In such cases, variation in the object velocity during the execution of the sequence may hamper the accuracy of the method. In this study, we have made a computer simulation of the performance of a phase mapping method sequence (TE = 46 msec) designed for quantitative studies of motion in brain tissue. Using a Gaussian-shaped velocity input function, the time shifting and the amplitude modulation properties of the sequence was studied for various values of the duration, defined as the full width of tenth of maximum (FWTM), of the input function. The time shift corresponded well to the center of the 180 degrees RF pulse, and the amplitude modulation was seen to decrease with increasing time duration of the velocity input function. Applied on in vivo data, where an approximately gaussian-shaped brain motion velocity pattern was assumed to have a duration of 150 msec, the amplitude modulation of the sequence was estimated to 2%.