We establish results concerning the existence and uniqueness of solutions to neutral stochastic functional differential equations with infinite delay and Poisson jumps in the phase space C((-?,0];Rd) under non-Lipschitz condition with Lipschitz condition being considered as a special case and a weakened linear growth condition on the coefficients by means of the successive approximation. Compared with the previous results, the results obtained in this paper is based on a other proof and our results can complement the earlier publications in the existing literatures.