A boiler-turbine unit is a typical multi-input multi-output (MIMO) industrial control system in power plant, which has nonlinear and couple characteristics. In this paper, a constrained dynamic matrix control (DMC) algorithm is designed for a nonlinear multivariable boiler-turbine unit with hard input constraints. Firstly an improved unconstrained DMC algorithm based on step response model for a single-input single-output (SISO) integrating process is proposed. It is shown that the proposed algorithm is more effective than conventional DMC and can also be extended to MIMO systems with integrating subsystems and input/output constraints. A 1-norm objective function is presented and the control actions can be obtained using linear programming on-line. Simulation results show that the designed control system has good tracking property and disturbance rejection ability without steady state offset while the control actions satisfy the constraints.