In this paper, we present a sequence quadratic semidefinite programming (SSDP) algorithm method without a penalty function or a filter for nonlinear  semidefinite programming. At each iteration, the search direction is determined by solving a specially quadratic semidefinite programming subproblem. The nonmonotone line search ensures that the objective function or constraint violation function is sufficiently reduced. The proposed algorithm is globally convergent under some mild conditions. The preliminary numerical results are reported at the end of the paper.