The secure operation of power systems is always the first aid in the power system operation. However, an economic operation of power systems in both the normal and contingency cases is always a goal to achieve for electric power system operators. This paper is dealing with the multi-objective security-constrained optimal active and reactive power dispatch (MO-SCOARPD) problem in power systems considering different objectives such as fuel cost, power losses, stability index, and voltage deviation with the worst scenarios of contingency analysis for transmission line outage to determine the best states for operation. The MO-SCOARPD is a very complex and large-scale problem due to handling many control variables in both normal and contingency cases. In this paper, a hybrid particle swarm optimization and differential evolution (HPSO-DE) has been implemented for solving the problem. The proposed HPSO-DE is a hybrid method to utilize the advantages of both PSO and DE methods for solving the complex and largescale optimization problems. Consequently, the new hybrid method is more effective than the DE and PSO in obtaining the optimal solution for the optimization problems. The effectiveness of the proposed HPSO-DE has been verified on the IEEE 30 bus system for different objectives and various scenarios of line outages. The obtained results have indicated that the proposed HPSO-DE method can find better solution quality than both DE and PSO methods for all cases. Therefore, the proposed HPSO-DE can be a very favorable and promising method for dealing with the complex and large-scale optimization problem in power systems such as the MO-SCOARPD problem.