In this paper, we study a stochastic recursive optimal control problem in which the objective functional is described by the solution of a backward stochastic differential equation driven by G-Brownian motion. Under standard assumptions, we establish the dynamic programming principle and the related Hamilton-Jacobi-Bellman (HJB) equation in the framework of G-expectation. Finally, we show that the value function is the viscosity solution of the obtained HJB equation.that Buckdahn et al. [2] obtained an existence result of the stochastic recursive optimal control problem.Motivated by measuring risk and other financial problems with uncertainty, Peng [22] introduced the notion of sublinear expectation space, which is a generalization of probability space. As a typical case, Peng studied a fully nonlinear expectation, called G-expectationÊ[·] (see [25] and the references therein), and the corresponding time-conditional expectationÊ t [·] on a space of random variables completed under the norm E[| · | p ] 1/p . Under this G-expectation framework (G-framework for short) a new type of Brownian motion called G-Brownian motion was constructed. The stochastic calculus with respect to the G-Brownian motion has been established. The existence and uniqueness of solution of a SDE driven by G-Brownian motion can be proved in a way parallel to that in the classical SDE theory. But the solvability of BSDE driven by G-Brownian motion becomes a challenging problem. For a recent account and development of G-expectation theory and its applications we refer the reader to [7,8,16,20,21,26,27,32,35,36]. Let us mention that there are other recent advances and their applications in stochastic calculus that do not require a probability space framework. Denis and Martini [3] developed quasi-sure stochastic analysis, but they did not have conditional expectation. This topic was further examined by Denis et al. [4] and Soner et al. [33]. It is worthing to point out that Soner et al. [34] have obtained a deep result of existence and uniqueness theorem for a new type of fully nonlinear BSDE, called 2BSDE. Various stochastic control (game) problems are investigated in [13, 17, 18, 30] and the applications in finance are studied in [14, 15]. Recently Hu et. al studied the following BSDE driven by G-Brownian motion in [11] and [10]: Y t = ξ + They proved that there exists a unique triple of processes (Y, Z, K) within our G-framework which solves the above BSDE under a standard Lipschitz conditions on f (s, y, z) and g(s, y, z) in (y, z). The decreasing G-martingale K is aggregated and the solution is time consistent. Some important properties of the BSDE driven by G-Brownian motion such as comparison theorem and Girsanov transformation were given in [10].In this paper, we study a stochastic recursive optimal control problem in which the objective functional is described by the solution of a BSDE driven by G-Brownian motion. In more details, the state equation is governed by the following controlled SDE driven by G-Brownian motion dX t,x,u s