This article presents an active fault-tolerant formation control method based on learning neural network approaches for elliptical orbit spacecraft with thruster faults. To approximate thruster fault/synthesized perturbation online, we propose a learning radial basis function neural network (RBFNN) model in which the iterative learning algorithm with one algebraic iteration is first adopted to update the weight matrix of the RBFNN. Compared with conventional adaptive RBFNN models, the proposed learning RBFNN model requires fewer computations and allows for discontinuous output measurement. A learning neural network sliding mode observer is explored to accurately and robustly reconstruct the thruster fault and estimate the relative state of the formation. Subsequently, a learning neural network sliding mode control (SMC) law is designed to achieve accurate fault-tolerant configuration tracking for maintenance, in which the learning RBFNN model is used to online approximate and compensate for synthesized perturbations. Compared with the nonlinear terminal SMC method, the proposed control approach exhibits higher tracking accuracy for configuration maintenance without requiring massive computation. Numerical simulations and detailed comparisons are provided to illustrate the feasibility and superiority of the presented spacecraft fault-tolerant formation control approach.