Based on the developed optically pumped graphene multilayer terahertz surface plasma structures, this paper calculates the real part of propagation index and amplification coefficient in optically pumped graphene multilayer structures, discusses the inluences of momentum relaxation time, temperature, numbers of grapheme layers, and the quasi-Fermi energy in the topmost grapheme layer on the real part of propagation index and amplification coefficient. It is shown that when the real part of dynamic conductivity becomes negative in the terahertz range of frequencies in the optically pumped graphene multilayer structures, the surface plasma of graphene layers can achieve gain. By comparing the peeling-graphene-structure with the graphene structure that has a high conducting bottom graphene layer in optically pumped scheme, it can be said that the surface plasma of the peeling-graphene-structure can get a high efficient amplification. Meanwhile, the structure having properly numbers of graphene layers can get a larger amplification than the simple graphene structure in an optically pumped scheme at low temperatures.