Distributed acoustic sensor (DAS), which utilizes the entire optical fiber as the sensing medium, provides distinct advantages of high resolution, dynamic monitoring, and resistance to high temperatures. This technology finds diverse applications in the seismic exploration, oil survey, and submarine cable monitoring industries. However, DAS signals are susceptible to various kinds of noise, such as horizontal noise, erratic noise, random noise, and so on, which significantly degrade the SNR. This low SNR is likely to affect some subsequent analyses, such as inversion and interpretation. The mixed noises feature of the DAS data poses a serious challenge for SNR enhancement. To address this issue, we develop a supervised learning-based densely connected residual convolutional denoising network (DCRCDNet), which leverages both encoding and decoding processes to extract features and reconstruct DAS data. The design of dense connectivity and residual blocks allow the network to extract both shallow and deep features. The network is trained using both synthetic and field data to obtain the optimal network parameters. Testing on synthetic data demonstrates that DCRCDNet improves the signal-to-noise ratio (SNR) from −10.21 dB to 15.61 dB. The test results from both synthetic and field data indicate that, compared to traditional filtering methods and other deep learning approaches, this network effectively suppresses noise in DAS signals. Consequently, DCRCDNet shows great potential in reconstructing DAS signals from hidden noise, suppressing strong and mixed noise, and extracting hidden signals.