Abstract: QISM algorithm requires that variables in the system must be continuous, so it can't solve the problem with different constraints in different states. PQSIM algorithm improves on this point. Two constraints are added to PQSIM, Constraint IF and Constraint EQ, to constrict the state sets effected by constraints. PQSIM can simulate the system with piecewise functions qualitatively and effectively. An instance is given to testify the correctness of this algorithm. At last we analyzed the complex of PQSIM to prove that it is a good algorithm.