This study suggests a novel quantum immune algorithm for finding Pareto-optimal solutions to multiobjective optimization problems based on quantum computing and immune system. In the proposed algorithm, there are distinct characteristics as follows. First, the encoding method is based on Q-bit representation, and thus a chaos-based approach is suggested to initialize the population. Second, a new chaos-based rotation gate and Q-gates are presented to perform mutation and improve the quality of the population, respectively. Finally, especially, a new truncation algorithm with similar individuals (TASI) is utilized to preserve the diversity of the population. Also, a new selection operator is proposed to create the new population based on TASI. Simulation results on six standard problems (ZDT6, CP, SP, VNT, OSY and KIT) show the proposed algorithm is able to find a much better spread of solutions and has better convergence near the true Pareto-optimal front compared to the vector immune algorithm (VIS) and the elitist non-dominated sorting genetic system (NSGA-II).