Crystal structure prediction (CSP) has emerged as one of the most important approaches for discovering new materials. CSP algorithms based on evolutionary algorithms and particle swarm optimization have discovered a great number of new materials. However, these algorithms based on ab initio calculation of free energy are inefficient. Moreover, they have severe limitations in terms of scalability. We recently proposed a promising crystal structure prediction method based on atomic contact maps, using global optimization algorithms to search for the Wyckoff positions by maximizing the match between the contact map of the predicted structure and the contact map of the true crystal structure. However, our previous contact-map-based CSP algorithms have two major limitations: (1) the loss of search capability due to getting trapped in local optima; (2) it only uses the connection of atoms in the unit cell to predict the crystal structure, ignoring the chemical environment outside the unit cell, which may lead to unreasonable coordination environments. Herein, we propose a novel multiobjective genetic algorithm for contact-map-based crystal structure prediction by optimizing three objectives, including contact map match accuracy, individual age, and coordination number match. Furthermore, we assign the age values to all the individuals of the GA and try to minimize the age, aiming to avoid the premature convergence problem. Our experimental results show that compared to our previous CMCrystal algorithm, our multiobjective crystal structure prediction algorithm (CMCrystalMOO) can reconstruct the crystal structure with higher quality and alleviate the problem of premature convergence. The source code is open sourced and can be accessed at https://github.com/usccolumbia/MOOCSP.