A new feasible QP-free algorithm for general nonlinear programming problems with only inequality constraints is proposed in this paper. The authors suggest a new working-set identification technique that has shown promising theoretical advantage. A standard global convergence result is given. More importantly, without the common strict complementarity assumption, the algorithm is shown to be locally superlinearly convergent under an assumption that is weaker than the strong second-order sufficient condition. Some preliminary numerical results are also presented.