A novel deep learning-based proportional multiple-integral (DL-PMI) observer is presented in this article to reconstruct actuator faults of quadrotors. The DL-PMI observer is composed of a deep neural network (DNN) observer, a nonlinear saturation function and a linear-parameter-varying-based PMI observer. The DNN observer is trained to provide an accurate actuator fault estimation, which is then introduced into the PMI observer as a correction term to improve the estimation accuracy. But in some untrained scenarios, the DNN observer estimation results may be inaccurate, leading to the estimation divergence of the DL-PMI observer. To deal with this problem, a nonlinear saturation function is designed to bound the estimation difference between the DNN observer and the PMI observer. Moreover, the PMI observer is designed based on the robust $\mathcal {H}_\infty$ method, which guarantees the estimation error of the DL-PMI observer is bounded. Finally, the convergence and robustness of the DL-PMI observer is proved based on Lyapunov theory. The experimental results demonstrate that the DL-PMI observer has higher estimation accuracy for actuator faults than the PMI observer while the convergence can still be guaranteed.