In this talk, a new sequential quadratically constrained quadratic programming (SQCQP) algorithm is presented for nonlinear programming. At each iteration of an SQCQP method, a quadratically constrained quadratic program (QCQP) subproblem is solved followed by a line search. If an l-infinity penalty function is used as a merit function, this method is shown to have global convergent property under the MFCQ and other mild conditions. No convexity assumptions are made concerning the objective and constraints. Finally numerical results from the CUTEst test collection will be given to justify our theoretical prediction.