This paper illustrates the Newton-Euler laws-based nonlinear dynamic model of a Crazyflie Quadrotor Unmanned Aerial Vehicle (CF-QUAV). It demonstrates the state-space-form equations that govern how the CF-QUAV moves around its frame (body). A Proposed nonlinear control strategy is used to regulate the height (z), position (x, y), attitude (roll and pitch), and heading (yaw) angles. This strategy is based on a Backstepping nonlinear controller defined by Lyapunov theory. The proposed controller can replace the Proportional-Integration-Derivative (PID) controller utilized in the CF-QUAV model to follow the desired trajectories gleaned from CF lab tests. In addition, the parameters of the proposed controller are tuned using the Genetic Algorithm (GA) in order to achieve the best performance and stability of the CF-QUAV model. Simulation-based experiments with statistical analysis are carried out to evaluate the performance of the proposed nonlinear controller and compare its performance and stability with the linear PID controller.