In sequence study, set-based analysis has been developed as a popular tool for analysing the association of a group rare variant with disease. However, most of the methods are sensitive to the genetic architecture. Besides, by directly combining the association signals of multiple markers within a genomic region can inevitably include a large proportion of noises. To address this issue, we extend the aggregated Cauchy association test (ACAT; Liu et al. 2019) and propose an adaptive Cauchy-variable combination method (ACC). Our proposed method combines Cauchy-variables, which are transformed from variant-level P-values in a given genomic region and adaptively truncate noises by choosing an optimal truncation threshold of the variant-level P-value that is determined by the data. Besides, the ACC method can use summary statistics obtained from open access database when the original genotype and phenotype data are unavailable. Extensive simulation studies and Genetic Analysis Workshop 19 real data analysis show that ACC is more powerful than the other comparative methods when only a small proportion of variants are causal, and ACC is robust to the varied genetic architecture.