In this paper, we propose a primal IP method for solving the optimal experimental design problem with a large class of smooth convex optimality criteria, including A-, D- and p th mean criterion, and establish its global convergence. We also show that the Newton direction can be computed efficiently when the size of the moment matrix is small relative to the sample size. We compare our IP method with the widely used multiplicative algorithm introduced by Silvey et al. . The computational results show that the IP method generally outperforms the multiplicative algorithm both in speed and solution quality.