Many intracellular transports are performed by multiple molecular motors in a cooperative manner. Here, we use stochastic simulations to study the cooperative transport by multiple kinesin motors, focusing mainly on effects of the form of unbinding rate versus force and the rebinding rate of single motors on the cooperative transport. We consider two forms of the unbinding rate. One is the symmetric form with respect to the force direction, which is obtained according to Kramers theory. The other is the asymmetric form, which is obtained from the prior studies for the single kinesin motor. With the asymmetric form the simulated results of both velocity and run length of the cooperative transport by two identical motors and those by a kinesin-1 motor and a kinesin-2 motor are in quantitative agreement with the available experimental data, whereas with the symmetric form the simulated results are inconsistent with the experimental data. For the cooperative transport by a faster motor and a much slower motor, the asymmetric form can give both larger velocity and longer run length than the symmetric form, giving an explanation for why kinesin adopts the asymmetric form of the unbinding rate rather than the symmetric form. For the cooperative transport by two identical motors, while the velocity is nearly independent of the rebinding rate, the run length increases linearly with the rebinding rate. For the cooperative transport by two different motors, the increase of the rebinding rate of one motor also enhances the run length of the cooperative transport. The dynamics of transport by *N* (*N* = 3, 4, 5, 6, 7 and 8) motors is also studied.