This paper focuses on designing an adaptive Radial basis function neural network (RBF NN) control method for an n-link robot manipulator in the presence of unknown parameters and disturbances. A minimum parameter learning method that observably reduces the online computational burden is used to estimate the maximum norm of ideal RBF NN weight vectors. The unknown disturbances are compensated by an exponential disturbance observer (asymptotic nonlinear disturbance estimator with exponential decaying error), which does not require the knowledge of the bound of disturbances and the measurement of acceleration signals. The closed-loop system is proved uniformly ultimately bounded with the developed adaptive RBF NN controller and disturbance observer. A two-link robot manipulator is taken for simulation. Both the theoretical analysis and simulations validate the effectiveness of the developed scheme.