The Pd39Ni10Cu30P21 bulk metallic glass is isothermally relaxed under various pressures. The degree of thestructural relaxation is evaluated in terms of the enthalpy recovery behaviours involved in the irreversible glasstransition processes by using a temperature-modulated differential scanning calorimetry technique. A roughlylinear increase of the recovery enthalpy is observed within the experimental pressure range from 2.67 to 4.45 Gpa,whih reflects the release of the frozen-in enthalpy in the as-quenched glass withincreasing relaxation pressure.The pressure dependence of the timescale of the enthalpy recovery processes is also exhibited.