Availability of affordable and accessible whole genome sequencing for biomedical applications poses a number of statistical challenges and opportunities, particularly related to the analysis of rare variants and sparseness of the data. Although efforts have been devoted to address these challenges, the performance of statistical methods for rare variants analysis still needs further consideration.We introduce a new approach that applies restricted principal component analysis with convex penalization and then selects the best predictors of a phenotype by a concave penalized regression model, while estimating the impact of each genomic region on the phenotype. Using simulated data, we show that the proposed method maintains good power for association testing while keeping the false discovery rate low under a verity of genetic architectures. Illustrative data analyses reveal encouraging result of this method in comparison with other commonly applied methods for rare variants analysis.By taking into account linkage disequilibrium and sparseness of the data, the proposed method improves power and controls the false discovery rate compared to other commonly applied methods for rare variant analyses.