We experimentally realize the enhancement of six-beam quantum squeezing by utilizing a six-beam phase-sensitive amplifier (PSA) based on cascaded four-wave mixing processes. Compared to the intensity-difference squeezing (IDS) of about 5.03 or 5.09 dB generated by a six-beam phase-insensitive amplifier (PIA), the six-beam IDS generated by the six-beam PSA is enhanced to about 6.64 dB. The intrinsic interference of six-beam PSA induces this enhancement. In addition, we investigate the dependence of IDS generated by the six-beam PSA and PIAs on the powers of two pump beams. The results show that the IDS of six-beam PSA is always better than that of six-beam PIAs. Our scheme may find potential applications in high-precision multi-parameter quantum metrology.