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In this paper,we investigate a priori error estimates and superconvergence properties for a model optimal control problem of bilinear type,which includes some parameter estimation application.The state and co-state are discretized by piecewise linear functions and control is approximated by piecewise constant functions.We derive a priori error estimates and superconvergence analysis for both the control and the state approximations.We also give the optimal L2-norm error estimates and the almost optimal L8-norm estimates about the state and co-state.The results can be readily used for constructing a posteriori error estimators in adaptive finite element approximation of such optimal control problems.