We simulate the strong ground motion generated from the earthquake rupture process on a shallow strike-slip fault using a 3D finite-difference method. The faulting process is modeled using a crack model with fixed rupture velocity. The variability of peak ground velocity patterns, correlated with fault location and source parameters such as stress drop or rupture velocity, is investigated. Our findings suggest that these patterns are strongly affected by rupture directivity and the uppermost depth of the fault or that of the asperity. When a fault breaks the ground surface, the peak ground velocity and the peak ground acceleration show a narrow region of strong motion. When a fault is buried under the ground, the high peak ground velocity zone of the fault-parallel component is apart from the fault trace by a distance comparable to the fault depth. On the other hand, the fault-normal peak ground velocity is a maximum along the fault trace. The fault length (or asperity length) is not so effective for peak ground velocities. The effect of heterogeneity in stress drop and rupture velocity on strong ground motion is also investigated. When stress drop is not uniform but increases linearly with depth from zero at the uppermost depth, the peak ground velocity is reduced. These results help better predict the strong ground motion generated from a potential fault.