In the present study, the fusion reactions induced by neutron-rich nuclei have been investigated using the improved quantum molecular-dynamics (ImQMD) model. First, the accuracy of the results was determined by using a set of parameters IQ3a for 16O+92Zr, 40Ca+46Ti and 16O+154Sm fusion excitation functions. The obtained results revealed that the measured fusion excitation function can be reasonably well reproduced. A comparison was also performed with the theoretical results based on the coupled-channel calculations. Then, the time evolution of densities for the 16O+59Co and 32S+92Zr reactions in which the target nuclei were neutron-rich were studied and the fusion cross sections were calculated dynamically. It was found that the fusion cross sections of these reactions at energies around the Coulomb barrier can be well reproduced by using the ImQMD modle.