In order to improve the kinetic stability of quadrotor unmanned aerial vehicles, the effect of mechanical and structural parameters on the system stability was studied. The process during yawing state is taken as an example for investigation. According to the calculation process of Lyapunov exponents based on the dynamical model, the key mechanical and structural parameters significantly influencing the dynamic stability were obtained. The method of Lyapunov exponents was adopted to establish the relationship between such key parameters and the motion stability, which was utilized to design the mechanical and structural parameters, and then to optimize the stability control system. Finally, the theoretical analysis was validated through experimental tests. Compared with the Lyapunov′s second method, the main advantage of this method is that it is easy to construct the process of calculating exponent, which makes the stability analysis for complicated nonlinear systems possible.