Quadrotors, like any dynamical system, are subjected to model uncertainties which may cause instability and inaccuracy in navigation. In addition, the presence of input constraints violates the affine property which, as a result, adds additional challenges and complicates designing the control system for quadrotors. In this paper, an adaptive nonlinear control algorithm is designed to overcome these difficulties for small size quadrotors. The proposed algorithm consists of an approximation technique using radial basis function neural network and a modified reference model. This allows the quadrotor to follow a defined path under the presence of external disturbances, actuator saturation and system uncertainties associated with system parameters including mass, inertia and force coefficients. Finally, the stability of the proposed algorithm is proven within the region of interest and validated using simulation.