Pressure is well known to significantly raise the superconducting transition temperature, Tc, in both iron pnictides and cuprate based superconductors. Little work has been done, however, on how pressure can affect the flux pinning and critical current density in the Fe-based superconductors. Here, we propose to use hydrostatic pressure to significantly enhance flux pinning and Tc in polycrystalline pnictide bulks. We have chosen Sr4V2O6Fe2As2 polycrystalline samples as a case study. We demonstrate that the hydrostatic pressure up to 1.2 GPa can not only significantly increase Tc from 15 K (underdoped) to 22 K, but also significantly enhance the irreversibility field, Hirr, by a factor of 4 at 7 K, as well as the critical current density, Jc, by up to 30 times at both low and high fields. It was found that pressure can induce more point defects, which are mainly responsible for the Jc enhancement. Our findings provide an effective method to significantly enhance Tc, Jc, Hirr, and the upper critical field, Hc2, for other families of Fe-based superconductors in the forms of wires/tapes, films, and single crystal and polycrystalline bulks.