A successive linearization method with flexible penalty is presented to solve a nonlinear semidefinite programming with nonlinear inequality constraints. The new method does not require the penalty function to be reduced and does not use filter technique. The storage of the filter set is avoided. The updating of the penalty parameter is flexible, which is only dependent on the message of the current iterate. The penalty parameter sequence corresponding to the successful iterate point does not need to increase monotonically. To decide whether the trial step can be accepted or not, the new method requires the measure of constraint violation to be improved or the value of the objective function to be improved within the measure of feasibility control. Under the usual assumptions, we prove that the algorithm is well defined and globally convergent. Finally, preliminary numerical results are reported.