We consider independent sampling from a two-component mixture distribution, where one component (called the parametric component) is from a known distributional family and the other component (called the non-parametric component) is unknown. This is a semi-parametric mixture distribution. We discretize the nonparametric component and estimate the parameters of this mixture model, namely the mixing proportion, the unknown parameters of the parametric component and the discretized non-parametric component. We define the maximum penalized likelihood (MPL) estimates of the mixture model parameters and then develop a generalized EM (GEM) iterative scheme to compute the MPL estimates. A simulation study and an example from biology are presented.