In recent years, the motion control for determining the load mass using a fixed-length cable suspension for a quadrotor has been extensively studied and notable progress has been made. However, in practical applications, the relationship between load mass and cable length can cause unpredictable disturbance to the quadrotor system. In order to improve the stability of the quadrotor in this case, we study the influence of the relationship between the mass of the quadrotor load and the cable length. At first, a nonlinear dynamics two-dimensional model of quadrotor with a suspended load is proposed. Then, a controller is designed within the neural network-based model predictive control (NNMPC) framework, where multiple constraints are set. Finally, four simulation cases show that the relationship between load mass and cable length has a notable impact on the quadrotor’s stability.