Effective prediction of wireless communication link quality is a necessity to choose the reliable routing of multi-hop Internet of things (IoT) communication. The main challenge for its inaccurate prediction is caused by the random characteristic of the signal-tonoise ratio time series. To address this problem, based on the analysis of the random characteristics of wireless communication links, a method of predicting the confidence interval of communication quality is proposed in this paper. Firstly, the signal-to-noise ratio time series of wireless link quality is decomposed into stationary sequence and noise sequence by wavelet decomposition method. The noise standard deviation sequence is obtained by the noise sequence. Then, the prediction model of stationary sequence and noise standard deviation sequence is proposed by using LSTM neural network. The confidence interval of communication link reliability is calculated by using the prediction results. Finally, by comparing the lower bound of confidence interval with the reliability standard, it can prejudge whether the reliability of current wireless link meets the requirements of power grid. Through the comparative study, the proposed method can either satisfy the requirements of the application of IoT of distribution grid or provides more accurate result in comparing with the state-of-the-art methods.