G protein-coupled receptors (GPCRs) constitute the largest family among human membrane proteins which are the important targets of many drugs on the market. An accurate annotation of the biological functions of GPCR proteins is key to understand their involved biological processes and drug-acting mechanisms. In our previous work, we found that protein function prediction problem can be formulated as a multi-instance multi-label learning (MIML) task. In this paper, we propose a novel method for predicting biological functions of G protein-coupled receptors by using a fast MIML learning called MIMLfast along with a hybrid feature. The hybrid feature consists of amino acid triple information, amino acid correlation information, evolutionary information, secondary structure correlation information, signal peptide information, disordered residue information, physical and chemical properties among GPCR domains. The experimental results show that our method achieves good performance which is superior to state-of-the-art multi-instance multi-label learning methods, multi-label learning methods and CAFA protein function prediction methods.