In real-world applications, the optimization problems usually include some conflicting objectives and subject to many constraints. Much research has been done in the fields of multiobjective optimization and constrained optimization, but little focused on both topics simultaneously. In this study we present a hybrid constraint handling mechanism, which combines the -comparison method and penalty method. Unlike original -comparison method, we set an individual -value to each constraint and control it by the amount of violation. The penalty method deals with the region where constraint violation exceeds the -value and guides the search toward the -feasible region. The proposed algorithm is based on a well-known multiobjective evolutionary algorithm, NSGA-II, and introduces the operators in differential evolution (DE). A modified DE strategy, DE/better-to-best-feasible/1, is applied. The better individual is selected by tournament selection, and the best individual is selected from an archive. Performance of the proposed algorithm is compared with NSGA-II and an improved version with a self-adaptive fitness function. The proposed algorithm shows competitive results on sixteen public constrained multiobjective optimization problem instances.