In this article, an 𝛼-variable model-free prescribed-time controller (𝛼(t)-MFPTC) is proposed for a nonlinear system with uncertainties and disturbances. First, an ultra-local model is employed to formulate the plant dynamic by using input and output data. Second, to observe the state variables and compensate for the lumped uncertainties, a linear extended state observer (LESO) is designed.Then, a corresponding LESO-based 𝛼-fixed model-free controller (LESO-iPD) is proposed. Third, based on LESO-iPD, a prescribed-time sub-controller (PTC) is adopted to converge tracking error within a prescribed finite time. Furthermore, an adaptive RBF neural network compensator is constructed to approximate and compensate for LESO error. Correspondingly, an 𝛼-fixed model-free prescribed-time controller (𝛼-MFPTC) is proposed. Fourth, based on 𝛼-MFPTC, a tracking error-based 𝛼-variable method is applied to improve the controller performance, and an 𝛼-variable model-free prescribed-time controller (𝛼(t)-MFPTC) is subsequently proposed. Moreover, stability and prescribed-time convergence of closed-loop system with 𝛼(t)-MFPTC are analyzed by using the Lyapunov theorem. Ultimately, to demonstrate the performance and effectiveness of the proposed control strategy, the numerical simulation with sliding mode control, LESO-iPD, 𝛼-MFPTC, and 𝛼(t)-MFPTC and co-simulation results on quadrotor have been obtained.