For Constrained Multi-Objective Optimization Problem （CMOP） with complex constraints， balancing the algorithm's convergence and diversity effectively while ensuring strict constraint satisfaction is a significant challenge. Therefore， a Dual-Population Dual-Stage Evolutionary Algorithm （DPDSEA） was proposed. In this algorithm， two independently evolving populations were introduced： the main and secondary populations， and the feasibility rules and an improved epsilon constraint handling method were used for updating， respectively. In the first stage， the main and secondary populations were employed to explore the Constrained Pareto Front （CPF） and the Unconstrained Pareto Front （UPF）， respectively， to obtain positional information about the UPF and the CPF. In the second stage， a classification method was designed to classify CMOPs based on positions of the UPF and the CPF， thereby executing specific evolutionary strategies for different types of CMOPs. Additionally， a random perturbation strategy was proposed to perturb the secondary population evolved near the CPF randomly to generate some individuals on the CPF， thereby promoting convergence and distribution of the main population on the CPF. Finally， experiments were conducted on LIRCMOP and DASCMOP test sets to compare the proposed algorithm with six representative algorithms： CMOES （Constrained Multi-Objective Optimization based on Even Search）， dp-ACS （dual-population evolutionary algorithm based on Adaptive Constraint Strength）， c-DPEA （Dual-population based Evolutionary Algorithm for constrained multi-objective optimization）， CAEAD （Constrained Evolutionary Algorithm based on Alternative Evolution and Degeneration）， BiCo （evolutionary algorithm with Bidirectional Coevolution）， and DDCMOEA （Dual-stage Dual-Population Evolutionary Algorithm for Constrained Multiobjective Optimization）. The results show that DPDSEA achieves 15 best Inverted Generational Distance （IGD） values and 12 best Hyper Volume （HV） values in 23 problems， demonstrating DPDSEA’s performance advantages in handling complex CMOPs significantly.