This paper proposes recurrent neuron networks (RNNs) for a fingerprinting indoor localization using WiFi. Instead of locating user's position one at a time as in the cases of conventional algorithms, our RNN solution aims at trajectory positioning and takes into account the relation among the received signal strength indicator (RSSI) measurements in a trajectory. Furthermore, a weighted average filter is proposed for both input RSSI data and sequential output locations to enhance the accuracy among the temporal fluctuations of RSSI. The results using different types of RNN including vanilla RNN, long short-term memory (LSTM), gated recurrent unit (GRU) and bidirectional LSTM (BiLSTM) are presented. On-site experiments demonstrate that the proposed structure achieves an average localization error of $0.75$ m with $80\%$ of the errors under $1$ m, which outperforms the conventional KNN algorithms and probabilistic algorithms by approximately $30\%$ under the same test environment.