This paper presents a new method to diagnose oil well pump faults using a modified radial basis function neural network. With the development of submersible linear motor technology, rodless pumping units have been widely used in oil exploration. However, the ground indicator diagram method cannot be used to diagnose the working conditions of rodless pumping units because it is based on the load change of the polished rod suspension point and its displacement. To solve this problem, this paper presents a new method that is applicable to rodless oil pumps. The advantage of this new method is its use of a simple feature extraction method and advanced genetic algorithm to optimize the threshold and weight of the RBF neural network. In this paper, we extract the characteristic value from the operation parameters of the submersible linear motor and oil wellhead as the input vector of the fault diagnosis model. Through experimental analysis, the proposed method is proven to have good convergence performance, high accuracy, and high reliability.