In order to overcome that the performance of sketch feature representation and recognition based on purely deep learning is not very well especially in limited sketch dataset, this paper proposes a feature representation of sketch based on the fusion of sparse coding and deep learning (FSCDL). Firstly, this method divides the sketch into components and extracts the features of sketch and sketch components with transfer deep learning. Then, it reduces the feature dimensions of the sketch and sketch components and clusters the sketch components. The cluster centers of sketch components are utilized to initialize the dictionary of sparse coding. Finally, the sketch feature representation is obtained by solving the objective function of sparse coding. Different from the previous work, this paper transfers deep learning to extract the features of sketches and sketch components, which are introduced to the sparse coding. The dictionary is initialized with the features obtained from the above transfer deep learning, which combines the semantic information obtained from deep learning and sparse coding. The proposed method not only improves the performance of the representation of the sketch, but also makes the sparse coding more interpretable. The experimental results show that the sketch recognition accuracy of the prposed method is higher than that of the traditional sketch feature representation methods and the sketch representation methods based on deep learning.