Gene-set analysis (GSA) aims to identify sets of differentially expressed genes by a phenotype in DNA microarray studies. Challenges occur due to the salient characteristics of the data: (1) the number of genes is far larger than the number of observations; (2) gene expression measurements, especially within each gene set, can be highly correlated; and (3) the number of gene sets that can be examined is large and increasing rapidly. These challenges call for gene-set testing procedures that have both efficiency in computation for large GSAs and high power in the presence of the high correlation. We propose a new GSA approach called Linear Combination Test (LCT), incorporating the covariance matrix estimator of gene expression into the test statistic. The proposed LCT and two other GSA methods, a modification of Hotelling's T2 using a shrinkage covariance matrix and our SAM-GS (Dinu et. al. 2007), the two methods that have been reported by Tsai and Chen (2009) to perform best in terms of power, are evaluated in simulation studies and a real microarray study. The LCT method is more computationally efficient than the modified Hotelling's T2 and approximates the superb power of the modified Hotelling's T2. LCT is slightly faster than SAM-GS, but more powerful, due to incorporating the covariance matrix estimator. An extra step to enhance the interpretation of GSA results is also proposed in the form of a hierarchical LC (HLC) testing procedure, providing scientists useful hierarchical information on gene sets that LCT identified as differentially expressed.