Pulsar candidate selection is an important step in the search task of pulsars. The traditional candidate selection is heavily dependent on human inspection. However, the human inspection is a subjective, time consuming, and error-prone process. A modern radio telescopes pulsar survey project can produce totally millions of candidates, so the manual selection becomes extremely difficult and inefficient due to a large number of candidates. Therefore, this study focuses on machine learning developed in recent years. In order to improve the efficiency of pulsar candidate selection, we propose a candidate selection method based on self-normalizing neural networks. This method uses three techniques: self-normalizing neural networks, genetic algorithm and synthetic minority over-sampling technique. The self-normalizing neural networks can improve the identification accuracy by applying deep neural networks to pulsar candidate selection. At the same time, it solves the problem of gradient disappearance and explosion in the training process of deep neural networks by using its self-normalizing property, which greatly accelerates the training process. In addition, in order to eliminate the redundancy of the sample data, we use genetic algorithm to choose sample features of pulsar candidates. The genetic algorithm for feature selection can be summarized into three steps: initializing population, assessing population fitness, and generating new populations. Decoding the individual with the largest fitness value in the last generation population, we can obtain the best subset of features. Due to radio frequency interference or noise, there are a large number of non-pulsar signals in candidates, and only a few real pulsar signals exist there. Aiming at solving the severe class imbalance problem, we use the synthetic minority over-sampling technique to increase the pulsar candidates (minority class) and reduce the imbalance degree of data. By using k-nearest neighbor and linear interpolation to insert a new sample between two minority classes of samples that are close to each other according to certain rules, we can prevent the classifier from becoming biased towards the abundant non-pulsar class (majority class). Experimental results on three pulsar candidate datasets show that the self-normalizing neural network has higher accuracy and faster convergence speed than the traditional artificial neural network in the deep structure, By using the genetic algorithm and synthetic minority over-sampling technique, the selection performance of pulsar candidates can be effectively improved.