Summary: For constrained optimization problem, a class of smooth penalty algorithm is proposed. It is put forward based on \(L_p\), a smooth function of a class of smooth exact penalty functions \(l_p, ~~p \in (0,1]\). Under the very weak condition, a perturbation theorem of the algorithm is set up. The global convergence of the algorithm is derived. In particular, under the hypothesis of generalized Mangasarian-Fromovitz constraint qualification, it is proved that when \(p= 1\), after finite iterations, all iterative points of the algorithm are feasible solutions of the original problem. When \(p\in (0,1)\), after finite iteration, all the iteration points are the interior points of feasible solution set of the original problem.