We investigate the relation of the critical current density (Jc) and the remarkably increased superconducting transition temperature (Tc) for the FeSe single crystals under pressures up to 2.43 GPa, where the Tc is increased by ~8 K/GPa. The critical current density corresponding to the free flux flow is monotonically enhanced by pressure which is due to the increase in Tc, whereas the depinning critical current density at which the vortex starts to move is more influenced by the pressure-induced magnetic state compared to the increase of Tc. Unlike other high-Tc superconductors, FeSe is not magnetic, but superconducting at ambient pressure. Above a critical pressure where magnetic state is induced and coexists with superconductivity, the depinning Jc abruptly increases even though the increase of the zero-resistivity Tc is negligible, directly indicating that the flux pinning property compared to the Tc enhancement is a more crucial factor for an achievement of a large Jc. In addition, the sharp increase in Jc in the coexisting superconducting phase of FeSe demonstrates that vortices can be effectively trapped by the competing antiferromagnetic order, even though its antagonistic nature against superconductivity is well documented. These results provide new guidance toward technological applications of high-temperature superconductors.