In the application of wireless sensor networks (WSNs) to smart grid, real-time and accurate wireless link quality prediction (LQP) is important to determine which link is reliable enough to undertake the communication task. However, the existing LQP methods are neither suitable to describe the dynamic stochastic features of link quality nor to ensure the validity of prediction results. In this paper, a random-vector-functional-link-based LQP (RVFL-LQP) algorithm is proposed. The algorithm selects the signal-to-noise ratio (SNR) as the link quality metric and decomposes the raw SNR sequence into the time-varying sequence and the stochastic sequence according to the analysis of wireless link characteristics. Then, the RVFL network is used to establish the prediction model of the time-varying sequence and the variance of the stochastic sequence. Lastly, the probability-guaranteed interval boundary of SNR is predicted, and the validity and practicability of prediction results are evaluated by comparative experiments and real-world application, respectively.