Through modification of unconstrained model algorithmic predictive control（PC）algorithm based on the impulse response model of the system，a novel predictive control algorithm of linearly constrained system（LCS-PC）was developed by using linear programming optimization technique.Theoretical analysis showed that LCS-PC possessed the same stability and robustness of PC.Simulation results of an atmospheric distillation column control demonstrated that LCS-PC could not only satisfy the linearly constrained requirements of the column，but also give better control response than PC and linear quadratic optimal state feedback（LQSF）control.Comparison with quadratic programming（QP），LCS-PC had higher computation efficiency，so it could satisfy the real time control requirements of industrial processes much better than QP.