Pedestrian dead-reckoning (PDR) technique has high accuracy in short-term positioning and is little affected by environments, but its cumulative error makes long-term positioning infeasible. Received signal strength (RSS) fingerprint positioning is immune to the cumulative error, but its poor radio signal propagation affected by indoor environments leads to a large positioning error. The extended Kalman filter (EKF) is widely applied to improve the two methods, but the approximation of nonlinearity still causes a large localization error. In this study, we propose a new approach based on neural networks for the Wi-Fi/PDR positioning fusion. The nonlinear mapping capability of back-propagation (BP) neural network is used to correct the EKF nonlinear approximation errors. Unlike the commonly used PDR algorithm, a series of pedestrian historical motion states are applied to train the long short-term memory (LSTM) and then make predictions. This method can significantly reduce cumulative errors in PDR. On-site experiments demonstrate that the proposed method achieves an average localization error of 1.18 m with 73% of the errors under 2 m, which outperforms EKF and unscented Kalman filter (UKF) by approximately 45% under the same test environment. Moreover, another fusion method using LSTM localization results as a priori information is described in this article. Different from the fusion at the resulting level of the previous method, this second method achieves the fusion at the algorithm level by limiting the Wi-Fi reference point (RP) search range through the LSTM localization results to reduce training and positioning time.