Abstract: In this paper,the gradient projection and penalty function are used to make optimization problems for inequality and equality constraints into optimination problem without constraints.The algorithm of perturbed gradient projcetion with aribitrary initial point for inequality and equality constrained problem is given,which can get a sort of gradient projection method in accurate search direction and step,when parameter δk is different chosed.It is proved to be convenient in application.The algorithm is gobally convergent under very weak conditions.