Network reliability is an important index to the provision of useful information for decision support in the modern world. There is always a need to calculate symbolic network reliability functions (SNRFs) due to dynamic and rapid changes in network parameters. In this brief, the proposed squeezed artificial neural network (SqANN) approach uses the Monte Carlo simulation to estimate the corresponding reliability of a given designed matrix from the Box-Behnken design, and then the Taguchi method is implemented to find the appropriate number of neurons and activation functions of the hidden layer and the output layer in ANN to evaluate SNRFs. According to the experimental results of the benchmark networks, the comparison appears to support the superiority of the proposed SqANN method over the traditional ANN-based approach with at least 16.6% improvement in the median absolute deviation in the cost of extra 2 s on average for all experiments.