Abstract: Processes of Ornstein-Uhlenbeck type, driven by positive compound Poisson processes, are considered in this paper. We are interested in parametric estimation of those processes based on discrete observations. The parameter of the stationary distribution is estimated by the method of moments, and a consistent and asymptotically normal estimator is provided. The theoretical study is also generalized to the superposition case. \newcommand\fundinfoThe research is supported by the National Natural Science Foundation of China (10901100) and the Science \& Technology Program of Shanghai Maritime University (20100135).