We have studied current-driven domain wall motion in modified Ga_0.95Mn_0.05As Hall bar structures with perpendicular anisotropy by using spatially resolved Polar Magneto-Optical Kerr Effect Microscopy and micromagnetic simulation. Regardless of the initial magnetic configuration, the domain wall propagates in the opposite direction to the current with critical current of 1~2x10^5A/cm^2. Considering the spin transfer torque term as well as various effective magnetic field terms, the micromagnetic simulation results are consistent with the experimental results. Our simulated and experimental results suggest that the spin-torque rather than Oersted field is the reason for current driven domain wall motion in this material.