Correlating genetic variations with phenotypic differences is one of the central problems in human genetics. Common variations, such as single nucleotide polymorphisms (SNPs), have been identified as contributing to phenotypes (e.g. disease susceptibilities). Recent studies show that complex diseases may be influenced by variants having relatively low allele frequencies. In this article, we focus on the scenario where multiple rare variants with moderate penetrances collectively influence a trait phenotype. Our new collapse-based approach, GraphSyn, collapses a subset of the given rare variants, which is different from most existing approaches which collapse all given ones. The criterion of collapsing is measured by identifying synchronization properties among variants. We also design a new sum-weighted statistic, which incorporates estimations of minor allelic frequencies (MAFs) and of synchronization measurement. To demonstrate our approach, we apply GraphSyn both to one actual candidate gene study dataset and to simulation data. Comparison with two existing approaches (RWA S and RareCover) demonstrates that our approach has higher statistical powers, when the group population attributed risk (group PAR) is low. The software package, GraphSyn is available at: http://www.engr.uconn. edu/∼jiw09003.