The smart grid will play an important role in the future city to support the diversified energy supply. Wireless communication, the most cost-effective alternative to the traditional wire-lines, promises to provide ubiquitous bi-direction information channel for smart grid devices. However, due to the complex environment that smart grid devices located in, the wireless link is easily been interfered with and therefore appears strong stochastic features. Considering different smart grid application traffics have different and strict reliability requirements, the confidence interval lower boundary is more suitable to represent the worst-case reliability of the stochastic wireless link quality and trustworthy for judging whether the link quality is qualified for the next transmission. In this paper, we propose a Long-Short-Term-Memory (LSTM) based link quality confidence interval lower boundary prediction for the smart grid. According to the analysis of the characteristics of the wireless link, we employ the wavelet denoising algorithm to decompose the signal-to-noise ratio time series into the deterministic part and the stochastic part for training two LSTM neural networks. Then, the deterministic part and the variance of the stochastic part are predicted respectively. Lastly the confidence interval boundary is calculated. To verify the performance of the proposed LQP method, real-world experiments are carried out and the results show that our method is more accurate and trustworthy in comparison with other link quality prediction methods.