Multi-Instance Multi-Label (MIML) learning is one of challenging research problems in machine learning. The main aim of this paper is to propose and develop a novel sparsity-based MIML learning algorithm. Our idea is to formulate and construct a transductive objective function for labels indicator to be learned by using the method of random walk with restart that exploits the relationships among instances and labels of objects, and computes the affinities among the objects. Then sparsity can be introduced in the labels indicator of the objective function such that relevant and irrelevant objects with respect to a given class can be distinguished. The resulting sparsity-based MIML model can be given as a constrained convex optimization problem, and it can be solved very efficiently by using the augmented Lagrangian method. Experimental results on benchmark data have shown that the proposed sparse-MIML algorithm is computationally efficient, and effective in label prediction for MIML data. We demonstrate that the performance of the proposed method is better than the other testing MIML learning algorithms.