We have observed directly the magnetic images of the dynamic motion of quantized interlayer vortices induced by the Lorentz force in an anisotropic high-Tc La1.87Sr0.13CuO4 single crystal. A scanning superconducting quantum interface device microscope is used for this study and it is found that three modes of flux motion exist depending on the transport current. By increasing the sample current‖c axis, a transition from the creeplike behavior to a steady flow of vortices was observed. Even higher current induced a continuous expansion of vortex-flow area depending on the inhomogeneity of the pinning force in a crystal.