Abstract Identifying rare variants that contribute to complex diseases is challenging because of the low statistical power in current tests comparing cases with controls. Here, we propose a novel and powerful rare variants association test based on the deviation of the observed mutation burden of a gene in cases from a baseline predicted by a weighted recursive truncated negative-binomial regression (RUNNER) on genomic features available from public data. Simulation studies show that RUNNER is substantially more powerful than state-of-the-art rare variant association tests and has reasonable type 1 error rates even for stratified populations or in small samples. Applied to real case-control data, RUNNER recapitulates known genes of Hirschsprung disease and Alzheimer's disease missed by current methods and detects promising new candidate genes for both disorders. In a case-only study, RUNNER successfully detected a known causal gene of amyotrophic lateral sclerosis. The present study provides a powerful and robust method to identify susceptibility genes with rare risk variants for complex diseases.