Biogeography-based optimisation (BBO) is a well-used nature-inspired algorithm in dealing with optimisation problems. In our previous work, we have applied this algorithm to multi-objective optimisation problems (MOPs) and termed the algorithm multi-objective biogeography-based optimisation (MOBBO). However, in the design of the original migration operator, a selected emigrant is supposed to be completely replaced by an immigrant, which makes the population diversity be apt to deteriorate. Therefore, the ability to approximate the true Pareto front will be weakened. To address this issue, in this paper, we design a velocity variable for each individual, which depicts the degree how immigrants affect emigrants. The positions of each individual which represents candidate solutions will be affected by their velocities. In this way, emigrants and immigrators' velocities are involved in one migration operator so that the population diversity maintains. We employ several classical benchmarks to compare the improved MOBBO with several other classical algorithms and the results demonstrate that the improved MOBBO with migration velocity is much competitive in addressing MOPs.