Detecting malware is a crucial defense mechanism against potential cyber-attacks. However, current methods illustrate significant limitations in achieving high performance while maintaining faster inference on edge devices. This study proposes a novel deep network with dual-attention feature refinement on a two-branch deep network to learn real-time malware detection on edge platforms. The proposed method introduces lightweight spatial-asymmetric attention for refining the extracted features of its backbone and multi-head attention to correlate learned features from the network branches. The experimental results show that the proposed method can significantly outperform existing methods in quantitative evaluation. In addition, this study also illustrates the practicability of a lightweight deep network on edge devices by optimizing and deploying the model directly on the actual edge hardware. The proposed optimization strategy achieves a frame rate of over 545 per second on low-power edge devices.