The aim of this research is to clarify a quantitative evaluation in the structural relaxation processes focusing on the activation energy on the addition of B to Cu-based amorphous alloys. The activation energy for structural relaxation process in a metal type amorphous CuHfTi ternary and CuHfTiB quaternary alloys, with cross sections of typically 0.03 mm x 2.0 mm, prepared by chill-block melt spinning has been investigated by Differential Scanning Calorimetry (DSC) with a cyclically heating technique. Activation energies for structural relaxation with a spatial quantity in amorphous materials have been discussed by use of a total relaxed ratio function that depends on annealing temperature and time. In the present work on CuHfTi ternary and CuHfTiB quaternary alloys, the distributions for the Activation Energy Spectrum (AES) by calculation with derivative-type relaxed ratio function were observed almost 160 kJmol-1, whereas in difference for shape only in the CuHfTi-B3% quaternary alloy. Another result has been also established that the ‘reversible’ AES model energy distribution though the cyclically structure relaxation occurs even in amorphous CuHfTiB alloy system.