Peng first introduced the notion of G-Brownian motion and G-expectation and established the stochastic calculus with respect to G-Brownian motion in 2006. In this paper, we investigate the stochastic optimal control problems under G-expectation and obtain dynamic programming principle. The value function is proved to be a viscosity solution of a fully nonlinear second-order partial differential equation. A particular case of this equation is the well-known Hamilton–Jacobi–Bellman–Isaacs equation. Copyright © 2011 John Wiley & Sons, Ltd.