Medication recommendation aiming at accurate prescription is a significant clinical application that assists caregivers in professional practice of medicine, and obtaining informative patient representations plays an important role in building effective recommendation models. Meanwhile, conducting attentive multi-hop reading on Memory Neural Network (MemNN) that stores knowledge from previous admissions is widely applied to derive contextual patterns for accurate patient representations. However, regular attentive reading may repeatedly attend to the same slots of MemNN. Although the coverage mechanism is proposed to tackle the problem, it is based on the assumption that there is one-to-one alignment between source information and target outputs, which medical records do not follow. In pursuit of a valuable model for medication recommendation, we propose the Multi-hop Reading with Selective Coverage (MRSC). MRSC firstly conducts information selection on MemNN based on the coverage of each slot. Then the method involves coverage into the attention calculation during the multi-hop reading on MemNN, making sure that all important historical records is fully utilized by balancing attention within selected information. Experiments on real-world clinical dataset demonstrate that MRSC successfully derives informative patient representations for the recommendation by conducting selection on MemNN and limiting attention adjustment within selected information.