Automatic hand-drawn sketch recognition is an important task in computer vision. However, the vast majority of prior works focus on exploring the power of deep learning to achieve better accuracy on complete and clean sketch images, and thus fail to achieve satisfactory performance when applied to incomplete or destroyed sketch images. To address this problem, we first develop two datasets that contain different levels of scrawl and incomplete sketches. Then, we propose an angular-driven feedback restoration network (ADFRNet), which first detects the imperfect parts of a sketch and then refines them into high quality images, to boost the performance of sketch recognition. By introducing a novel "feedback restoration loop" to deliver information between the middle stages, the proposed model can improve the quality of generated sketch images while avoiding the extra memory cost associated with popular cascading generation schemes. In addition, we also employ a novel angular-based loss function to guide the refinement of sketch images and learn a powerful discriminator in the angular space. Extensive experiments conducted on the proposed imperfect sketch datasets demonstrate that the proposed model is able to efficiently improve the quality of sketch images and achieve superior performance over the current state-of-the-art methods.