Aftershocks refer to the smaller earthquakes that occur following large earthquakes, in the same area of the main shock. The task of aftershocks detection, as a crucial and challenging issue in disaster monitoring, has attracted wide research attention in relevant fields. Compared with the traditional detection methods like STA/LTA algorithms or heuristic matching, neural network techniques are regarded as an advanced choice with better pattern recognition ability. However, current neural network-based solutions mainly formulate the seismic wave as ordinary time series, where existing techniques are directly deployed without adaption, and thus fail to obtain competitive performance on the intensive and highly-noise waveforms of aftershocks. To that end, in this paper, we propose a novel framework named Multi-Scale Description based Neural Network (MSDNN) for enhancing aftershock detection. Specifically, MSDNN contains a delicately-designed network structure for capturing both short-term scale and long-term scale seismic features. Therefore, the unique characteristics of seismic waveforms can be fully-exploited for aftershock detection. Furthermore, a multi-task learning strategy is introduced to model the seismic waveforms of multiple monitoring stations simultaneously, which can not only refine the detection performance but also provide additionally quantitative clues for discovering homologous earthquakes. Finally, comprehensive experiments on the data set from aftershocks of the Wenchuan M8.0 Earthquake have clearly validated the effectiveness of our framework compared with several state-of-the-art baselines.