Addressing the defects of slow convergence and low solution precision with multi-objective firefly algorithm, we propose a multi-objective firefly algorithm based on archive learning. The algorithm saves the elite particles obtained from each generation in an external archive and then randomly selects a particle from the external file as the learning object of the firefly to participate in the population evolution. The algorithm was verified by four test functions ZDT1, ZDT2, ZDT3 and ZDT6 and evaluated by IGD comprehensive evaluation index. Experiments have shown that the modified firefly algorithm does not only have a higher ability to escape from local optima, but also displays a significant improvement in convergence speed and solution precision. Our algorithm is more suitable for multi-objective optimisation problems that have a higher complexity. When applied to robot path planning, our modified algorithm can yield shorter length and higher smoothness of the path.