Continuous berth allocation problem (BAPC) is a major optimization problem in transportation engineering. It mainly aims at minimizing the port stay time of ships by optimally scheduling ships to the berthing areas along quays while satisfying several practical constraints. Most of the previous literatures handle the BAPC by heuristics with different constraint handling strategies as it is proved NP-hard. In this paper, we transform the constrained single-objective BAPC (SBAPC) model into unconstrained multiobjective BAPC (MBAPC) model by converting the constraint violation as another objective, which is known as the multiobjective optimization (MOO) constraint handling technique. Then a bias selection modified non-dominated sorting genetic algorithm II (MNSGA-II) is proposed to optimize the MBAPC, in which an archive is designed as an efficient complementary mechanism to provide search bias toward the feasible solution. Finally, the proposed MBAPC model and the MNSGA-II approach are tested on instances from literature and generation. We compared the results obtained by MNSGA-II with other MOO algorithms under the MBAPC model and the results obtained by single-objective oriented methods under the SBAPC model. The comparison shows the feasibility of the MBAPC model and the advantages of the MNSGA-II algorithm.