Deep Neural Network (DNN) assisted activity monitoring algorithms are investigated, aiming to discriminate three activity states, including presence without movement, nobody in bed, and presence with movement. The signal is collected from a fiber-based Mach-Zehnder Interferometer (MZI) sensor, which is placed under a 20-cm thick mattress. When people are lying on the mattress, cardiopulmonary activities will lead to the change of the phase difference of the MZI optical fiber sensor. In this paper, three kinds of DNNs are developed to investigate the classification performance, including feedforward neural network (FNN), convolutional neural network (CNN), and long short-Term memory network (LSTM). The accuracy of FNN, CNN and LSTM is 95.14%, 99.01%, and 99.37% within one second, respectively. Moreover, LSTM has low time and space complexity and better performance. The algorithms constructed can obtain high accuracy and robustness with low computational overhead and storage consumption and have broad application prospects. What's more, the MZI optical fiber sensor has many advantages such as low cost and anti-electromagnetic interference, which means that the system can be popular in medical treatment and households.