abstract: We study a class of stochastic optimal control problems where the drift term of the equation has a linear growth on the control variable, the cost functional has a quadratic growth and the control process takes values in a closed set (not necessary compact). This problem is related to some backward stochastic differential equations with quadratic growth and unbounded terminal value. We prove that the optimal feedback control exists and the optimal cost is given by the initial value of the solution of the related backward stochastic differential equation. (joint work with M. Fuhrman and Y. Hu).