Due to the gapless energy spectrum and carriers relaxation characteristics, graphene causes a widespread concern in amplification of terahertz coherent sources. We consider the contribution of both interband and intraband transitions to the conductivity, and study the dynamic conductivity characteristics of a nonequilibium two-dimensional electron-hole system in optically pumped single and multiple graphene layer (SGL and MGL) structures. The results demonstrate that the population inversion in graphene can lead to a negative dynamic conductivity in the terahertz range of frequencies at sufficiently strong pumping, and the phenomenon might be used in graphene-based terahertz coherent sources radiation and amplification. Meanwhile, by studying the dependences of the negative conductivity on momentum relaxation time, temperature, number of layers, and optical intensity, it is found that the minimum absolute value of the real part of conductivity in MGL structures is greater than that in SGL structures. Thus, the MGL structures have more advantages to be the active medium of terahertz laser.