In the paper, we study a model which is that the particles move forward inside the two parallel lanes with the same hopping probabilities p (0<p<1) and jump only one direction between the both lanes by theoretical means. When the system is in the stationary-state, we can calculate currents, density profiles and phase diagrams by an approximate theoretical approach. The system includes seven stationary-state phases, there is an interesting phenomenon that when hopping probabilities become small, except the (MC, MC) phase, the region of all other phases decrease. This model can help us to understand the effect of traffic system when the speed of vehicles decreases better. Computer simulation is used to simulate the results. It can be found that the theoretical results are in excellent agreement with Monte Carlo computer simulations.