The notion of g-expectations was first introduced by S.Peng via a class of nonlinear backward stochastic differential equations (BSDEs). He showed that g-expectations preserve many of the basic properties of the convenient mathematical expectations and conditional expectations except linearity. He also raised the question about the integral representation of g-expectation- s. In this paper, we try to investigate Peng's question and give a necessary and sufficient condition under which g-expectations can be represented by a Choquet integral.