The authors have studied the effects of pressure on the magnetocaloric effect in a polycrystalline La Fe _11.6 Si _1.4 sample. The Curie temperature T_C of the sample rapidly decreases from 191 K at ambient pressure to 80 K under 8.3 kbar pressure. The metamagnetic transition induced by field at temperatures above T_C becomes extremely sharp under high pressure and the critical field H_c of the transition increases fast with increasing temperature. As a result, the giant magnetocaloric effect in La Fe _11.6 Si _1.4 is greatly enhanced by pressure, especially at low magnetic fields. For a field variation of 1 T only, the maximum value of the entropy change is as high as 34 J / kg K .