Abstract We perform numerical simulations for the coupled sine-Gordon equation in order to investigate collective Josephson vortex dynamics under the presence of the c-axis parallel transport current and the ab-plane parallel magnetic field. The simulations reveal that Josephson vortices change their own flowing lattice structures with increasing the transport current. When the vortex density is high enough the structural transition voltages almost coincide with resonant points with transverse Josephson plasma modes. On the other hand, the coincidences fail with decreasing the vortex density and chaotic and more complicated flow patterns appear in low current regions. In both high and low vortex densities, we confirm that useful rectangular lattice flow states exciting the in-phase electromagnetic field oscillations can appear in high current regions.