This paper proposes an optimal energy management approach for a grid-connected microgrid (MG) by considering the demand response (DR). The multi-objective optimization framework involves minimizing the operating cost and maximizing the utility benefit. The proposed approach combines confidence-based velocity-controlled particle swarm optimization (CVCPSO) (i.e., PSO with an added confidence term and modified inertia weight and acceleration parameters), with a fuzzy-clustering technique to find the best compromise operating solution for the MG operator. Furthermore, a confidence-based incentive DR (CBIDR) strategy was adopted, which pays different incentives in different periods to attract more DR participants during the peak period and thus ensure the reliability of the MG under the peak load. In addition, the peak load shaving factor (PLSF) was employed to show that the reliability of the peak load had improved. The applicability and effectiveness of the proposed approach were verified by conducting simulations at two different scales of MG test systems. The results confirm that the proposed approach not only enhances the MG system peak load reliability, but also facilitates economical operation with better performance in terms of solution quality and diversity.