In this paper, we propose a small-footprint wake-upword speech recognition (WUWSR) system based on long shortterm memory (LSTM) recurrent neural network, and we design a novel back-end calibration scoring method named modified zero normalization (MZN). First, LSTM is trained to predict posterior probability of context-dependent state. Next, MZN is adopted to transfer posterior probability to normalized score, which is then converted to confidence score by dynamic programming. Finally, a certain wake-up-word is recognized according to the confidence score. This WUWSR system can recognize multiple wake-up words and change wake-up words flexibly. This system can guarantee low latency by omitting decoding network. Equal error rate (EER) is adopted as the evaluation metric. Experimental results show that the proposed LSTM-based system achieves 33.33% relative improvement compared with a baseline system based on deep feed-forward neural network. Combining the front-end LSTM acoustic model with back-end MZN method, our WUWSR system can achieve 51.92% relative improvement.