This paper is devoted to the design of a trajectory-following control for a differentiation nonholonomic wheeled mobile robot. It suggests a kinematic nonlinear controller steer a National Instrument mobile robot. The suggested trajectory-following control structure includes two parts; the first part is a nonlinear feedback acceleration control equation based on back-stepping control that controls the mobile robot to follow the predetermined suitable path; the second part is an optimization algorithm, that is performed depending on the Crossoved Firefly algorithm (CFA) to tune the parameters of the controller to obtain the optimum trajectory. The simulation is achieved based on MATLAB R2017b and the results present that the kinematic nonlinear controller with CFA is more effective and robust than the original firefly learning algorithm; this is shown by the minimized tracking-following error to equal or less than (0.8 cm) and getting smoothness of the linear velocity less than (0.1 m/sec), and all trajectory- following results with predetermined suitable are taken into account. Stability analysis of the suggested controller is proven using the Lyapunov method.