This paper proposes an efficient density estimation method for analyzing grouped data when local moments are given. We use the generalized method of moments (GMM) estimator of Hansen (1982) to incorporate the information contained in the local moments. We show that our estimator is more efficient than the classical maximum likelihood estimator for grouped data. We also construct a specification test statistic based on moment conditions. Monte Carlo experiments suggest that our estimator performs remarkably well and the specification test has good size properties even in finite samples.