Distributed acoustic sensing (DAS) technology has been widely used in seismic exploration to acquire high-quality data due to its noteworthy advantages, including high coverage, high resolution, low cost, and strong environmental friendliness. However, the seismic signals acquired in DAS are often masked by various types of noise (e.g., high-frequency random, high-amplitude erratic, horizontal, and coupled noise), which seriously decreases the signal-to-noise ratio (S/N). We propose a fully connected neural network with dense and residual connections to attenuate various complex noise in real DAS data. The network is designed to learn the features of useful reflection signals and remove various noise in an unsupervised way, therefore enjoying the convenience of label-free processing. The proposed network uses several encoders and decoders to compress and reconstruct the abstract waveform features, respectively. Each encoder/decoder consists of one dense block with stacked fully connected blocks. To transfer the shallow-level features to the deep-level for reusing, we add the skip connections with one fully connected block between the corresponding encoders and decoders. The proposed method provides encouraging results when applied to both synthetic and real DAS datasets. Compared with several traditional and advanced deep learning methods, our proposed method can more effectively attenuate strong noise and better extract hidden signals.