Distributed optical fiber sensor has been intensively researched owing to its various advantages, such as long monitoring distance, better sensing accuracy and spatial resolution. It has been widely applied in power cables, oil pipelines, transportation. Among the numerous kinds of distributed optical fiber sensors, Brillouin Optical Time-Domain Analyzer (BOTDA) attracts much attention due to its precise measurement for the temperature and strain in ultra-long sensing range. BOTDA is based on the effect of Simulated Brillouin Scattering (SBS), frequency difference between Brillouin scattering light and incident light is defined as Brillouin Frequency Shift (BFS), which is a linear function of temperature and strain. BFS is usually determined by finding the central frequency, which is with the maximum amplitude of the local Brillouin gain spectrum. However, in order to obtain Brillouin gain spectrum in long-distance monitoring applications, BOTDA needs to scan in frequency range around the Brillouin frequency of the optical fiber, so that a number of time-domain traces associated with each frequency are measured to ensure measurement accuracy, which will lead to tradeoffs among measurement accuracy and real-time performance. To enhance both the processing time and sensing accuracy, in recent years, machine learning and deep neural network have been widely proposed and introduced to BOTDA to extract temperature distribution from the measured Brillouin gain spectrum along the sensing fiber. The temperature extraction can be considered as a nonlinear regression problem and the regression model is constructed by learning from the spectrum samples using learning algorithms. Unlike other methods with the shallow architectures, deep neural network is composed of multiple processing layers that can learn representations of data with multiple levels of abstraction. Among many methodological variants of deep learning, Recurrent Neural Network (RNN) has achieved impressive performance in various challenging areas. By adding the time hidden layer into the architecture, RNN acquired better accuracy for sequential data due to the consideration of sequence characteristics. However, RNN has the problem of gradient disappearance. Therefore, we adopt a deep network called Long Short Term Memory (LSTM) for the temperature extraction of Brillouin gain spectrum. LSTM is a variation of RNN architecture that is overcome the problems of gradient disappearance and explosion, is particularly suitable to input sequences. In this paper, the data set is generated by using Lorentz function for LSTM network training, and the mapping relationship between LSTM network and temperature was established. A 40km BOTDA setup for temperature sensing is built to verify the performance of the trained LSTM. BOTDA that operates over a long sensing fiber is prone to be affected by the detrimental non-Local Effects (NLE), since NLE can distort Brillouin gain spectrum, therefore correctly retrieving BFS is very challenging. The experimental setup that we used to acquire data has distortion phenomenon in long distance temperature monitoring. We firstly use the spectral line subtraction method to correct the distorted Brillouin gain spectrum, the corrected Brillouin gain spectrum appears Lorentz shape, then leverage LSTM to learn the feature of the corrected Brillouin gain spectrum, finally, by feeding the Lorentz spectrum sequentially into the well-trained LSTM model, the temperature information along the sensing fiber of Brillouin spectrum can be quickly determined. The performance of LSTM is investigated both in simulation and experiment under different cases of frequency scanning steps, compared with classical ELM algorithm and curve fitting methods, the LSTM algorithm shows that the minimum root mean square error is 0.11℃. Besides, LSTM network has good robustness to frequency step change, even under the circumstance of large frequency step, the method still has good measurement accuracy, which improves the real-time performance of Brillouin optical time-domain temperature sensing system.