Zhou and Li [49] by virtue of stochastic linear-quadratic control theory studied the optimal portfolio problems with the asset price process satisfying a diffusion stochastic differential equation, and proposed the celebrated LQ framework and the efficient frontier for the given portfolio problem. We consider the optimal portfolio problems based on the asset price process satisfying a jump-diffusion stochastic differential equation. Similarly, we also arrive at the efficient frontier of the optimal portfolio selection problem. The conclusions obtained here can be regarded as a natural generalization of the work by Zhou and Li [49].