The similarity-based residual life prediction (SbRLP) approach is an important data-driven residual useful life (RUL) prediction technique. However, the accuracy and efficiency of local similarity measurements are not balanced, and the global similarity among samples are not considered in existing studies, thus limiting the application of the SbRLP method in big data environments. Hence, a novel SbRLP approach based on compound similarity is proposed here. First, the global and local similarities among samples are measured using the weighted Hausdorff distance and cosine adjustment similarity. Second, the global and local similarities are combined to measure the compound similarity based on the similarity control coefficient U. The best U is obtained via a parameter-selection method based on failure reference samples and the golden parabola method. Third, according to compound similarity, the RUL is predicted using the SbRLP method. Eventually, the effectiveness and superiority of the proposed SbRLP method are demonstrated with a small-sample case (i.e., gyroscope RUL estimation) and a large-sample case (i.e., engine RUL estimation). Results show that the proposed SbRLP method offers better prediction performance for the large-sample case. Additionally, the RUL can be estimated more accurately by adopting the best U obtained using the proposed parameter-selection method.