Abstract: In this paper,the gradient projection and penalty function are used to make optimization problems for inequality and equality constraints into optimization problems without constraints.An algorithm of perturbed gradient projection for inequality and equality constrained problems is given.Considering the error of calculating and perturbing in search direction,a gradient projection method for inexact search direction is produced,which can get a sort of gradient projection algorithm when parameter Wk is differently chosed.The algorithm is globally convergent under very weak conditions.