Multi-Instance (MI) learning has been proven to be effective for the genome-wide protein function prediction problems where each training example is associated with multiple instances. Many studies in this literature attempted to find an appropriate Multi-Instance Learning (MIL) method for genome-wide protein function prediction under a usual assumption, the underlying distribution from testing data (target domain, i.e., TD) is the same as that from training data (source domain, i.e., SD). However, this assumption may be violated in real practice. To tackle this problem, in this paper, we propose a Multi-Instance Metric Transfer Learning (MIMTL) approach for genome-wide protein function prediction. In MIMTL, we first transfer the source domain distribution to the target domain distribution by utilizing the bag weights. Then, we construct a distance metric learning method with the reweighted bags. At last, we develop an alternative optimization scheme for MIMTL. Comprehensive experimental evidence on seven real-world organisms verifies the effectiveness and efficiency of the proposed MIMTL approach over several state-of-the-art methods.