Most existing studies focused on the conflict between objective optimization and constraint satisfaction when solving constrained multi-objective optimization problems (CMOPs). However, as constraints become increasingly varied, they can exert different influence levels on the optimization process. Addressing this gap, this article proposes a constraint ranking and multitask-assisted constrained multi-objective evolutionary algorithm (CR-MT-CMOEA). CR-MT-CMOEA proposes a constrained ranking strategy to rank all constraints based on their influence levels, where a constraint with a greater influence will be assigned a higher rank and handled in a higher priority. After the constraint ranking, CR-MT-CMOEA adopts a multi-task optimization framework to handle all ranked constraints one by one by based on their priorities. The multitask-assisted framework could dynamically relax the constraint boundary and enhance the population convergence and diversity through co-evolution. The constrained ranking strategy and the multi-task optimization framework ensure that CR-MT-CMOEA could effectively solve CMOPs with multiple complex constraints. CR-MT-CMOEA is tested against seven CMOEAs on three test suites and 12 real-world problems. The experimental results demonstrate that CR-MT-CMOEA has significantly better performance.