Nonlinear evolutions of electrostatic shocks excited by a velocity-modulated ion beam along a magnetized plasma column are investigated by computer simulation for a Q-machine experiment. In the case of a beam velocity modulation, the perturbations grow spatially with subsequent saturation due to an ion bunching of the beam. With an increase in modulation ratio an electrostatic shock is formed, accompanied with a steepening of the propagating front. In the case of a beam density-modulation, however, the initial density jump decays simply. The velocity modulation method is quite effective for an excitation of electrostatic shocks in the Q-machine plasma with finite Landau damping. The simulation results using velocity modulation are consistent with the experimental results.