The paper presents a conjugate gradient-based numerical algorithm for optimal control of nonlinear multivariable systems with control and state vectors constraints. The algorithm has a backward-in-time recurrent structure similar to the backpropagation-through-time (BPTT) algorithm. The emphasis is on implementation and testing of various conjugate gradient methods. A vehicle dynamics control example demonstrates that the use of conjugate gradient algorithm leads to substantial reduction of computational time when compared to the standard gradient algorithm with a constant learning rate.