Abstract: The cutter suction dredger is an important equipment for land reclamation and port development, which is developing towards automation and intelligence. It is the current research hotspot to ensure the stability of the output slurry concentration by control the traverse speed. The slurry concentration during the operation of the dredger is affected by complex factors such as soil quality, environment, and working conditions. It is difficult to describe the control process with an exact mathematical model. This article collects data for the actual ship of the cutter suction dredger. By using the lateral speed of the dredger as input and the slurry concentration as output, a linear regression algorithm is used to establish the control model of the dredger traverse process. And apply this model to the design of subspace identification predictive controller. In the simulation of the control system, the simulation results show that the designed traverse process controller can make the system fast and stable under the appropriate parameters, when the control quantity is restricted. Thus, a stable output of slurry concentration is ensured and the dredging efficiency of the dredger is improved.