Modern techniques in the Internet of Things or autonomous driving require more accuracy positioning ever. Classic location techniques mainly adapt to outdoor scenarios, while they do not meet the requirement of indoor cases with multiple paths. Meanwhile as a feature robust to noise and time variations, Channel State Information (CSI) has shown its advantages over Received Signal Strength Indicator (RSSI) at more accurate positioning. To this end, this paper proposes the neural network method to estimate the centimeter-level indoor positioning with real CSI data collected from linear antennas. It utilizes an amplitude of channel response or a correlation matrix as the input, which can highly reduce the data size and suppress the noise. Also, it makes use of the consistency in the user motion trajectory via Recurrent Neural Network (RNN) and signal-noise ratio (SNR) information, which can further improve the estimation accuracy, especially in small datasize learning. These contributions all benefit the efficiency of the neural network, based on the results with other classic supervised learning methods.