This paper deals with the solution of the optimization with nonlinear inequality constraint. Based on the norm-relaxed sequential quadratic programming (SQP) method and the method of strongly sub-feasible directions, an SQP algorithm with active set identification technique is proposed. At each iteration, the norm-relaxed quadratic programming subproblem only consists of the constraints corresponding to an active identification set. Without any penalty parameters, the line search tech-nique can help combine the initialization phase with the optimization phase. The global convergence is proved under the Mangasarian-Fromovitz constraint qualifica-tion. If the second order su?cient conditions are satisfied, the proposed algorithm is strongly convergent and the active constraints are exactly identified by the iden-tification sets. The preliminary numerical results are also reported.