Here we report a pressure-induced reemergence of superconductivity in recently discovered superconductor K2Mo3As3, which is the first experimental case observed in quasi-one-dimensional superconductors. We find that, after full suppression of the ambient-pressure superconducting (SC-I) state at 8.7 GPa, an intermediary non-superconducting state sets in and prevails to the pressure up to 18.2 GPa, however, above this pressure a new superconducting (SC-II) state appears unexpectedly. High pressure x-ray diffraction measurements demonstrate that the pressure-induced dramatic change of the lattice parameter c contributes mainly to the emergence of the SC-II state. Combined with the theioretical calculations on band strcture, our results suggest that the reemergemce of superconductivity is associated with the change of the complicated interplay among different orbital electrons, driven by the pressure-induced unisotropic change of the lattice.