Constraint reduction is an essential method because the computational cost of the interior point methods can be effectively saved. Park and O'Leary proposed a constraint-reduced predictor-corrector algorithm for semidefinite programming with polynomial global convergence, but they did not show its superlinear convergence. We first develop a constraint-reduced algorithm for semidefinite programming having both polynomial global and superlinear local convergences. The new algorithm repeats a corrector step to have an iterate tangentially approach a central path, by which superlinear convergence can be achieved.