High critical current density (Jc) values in superconducting wires/tapes are desirable for high magnetic field applications. Recently developed pnictide wires/tapes exhibit exceptional superconducting properties such as high critical temperature (Tc), upper critical field (Hc2), and almost field-independent Jc. Despite the great fabrication efforts, however, the newly discovered pnictide wires/tapes are still not able to replace low-temperature superconductors such as Nb3Sn, due to their inferior Jc values. Ag-clad Sr0.6K0.4Fe2As2 tapes have demonstrated significant superconducting performance, although their low Jc in comparison to Nb3Sn is still a major challenge. By successfully employing hydrostatic pressure, a remarkably significant enhancement of Jc by an order of magnitude can be achieved in Sr0.6K0.4Fe2As2 tapes in both low and high fields. This is a promising technological step forward towards high-field applications, as the record high Jc values (∼2×105A/cm2 at 4.2 K and 13 T, P=1.1GPa) obtained for Sr0.6K0.4Fe2As2 tape are superior to those of Nb3Sn and other pnictide wires/tapes. Here, we used magnetic Jc data for comparison to the other reported transport Jc data, due to the lack of transport measurement facility under hydrostatic pressure. Our systematic analysis shows that pressure-induced pinning centers are the main source of Jc enhancement, along with a fractional contribution from geometric changes around the grain boundaries under pressure. We expect that utilization of an appropriate pressure approach will be a way to significantly enhance Jc to beyond the cutoff (maximum) values in various superconductors produced using other existing methods for Jc enhancement.