Recently, Convolutional Neural Network (CNN) and Long short-term memory (LSTM) based models have been introduced to deep learning-based target speaker separation. In this paper, we propose an Attention-based neural network (Atss-Net) in the spectrogram domain for the task. It allows the network to compute the correlation between each feature parallelly, and using shallower layers to extract more features, compared with the CNN-LSTM architecture. Experimental results show that our Atss-Net yields better performance than the VoiceFilter, although it only contains half of the parameters. Furthermore, our proposed model also demonstrates promising performance in speech enhancement.