In this talk, by a variational method and a filtering technique, a stochastic maximum principle for partially-observed optimal control problem with delay is developed. Also, a sufficient condition without assumption of the concavity is presented. Our results are applied to an example of investment problem. By a discretization technique, numerical scheme for forward-backward stochastic differential equations (FBSDEs) with delay and anticipate terms is proposed, and its numerical simulation is shown. Also, a linear quadratic control problem is given, which is not a special case of the above one. At last, by HJB equation, explicit expressions for the optimal value functions and the corresponding optimal strategies are obtained. Furthermore, both full and partial information schemes are simulated and compared. i.e., the utility is higher in the full information case than it in the partial case.