Over the past years, genome-wide association studies (GWAS) have generated a wealth of new information. Summary data from many GWAS are now publicly available, promoting the development of many statistical methods for association studies based on GWAS summary statistics, which avoids the increasing challenges associated with individual-level genotype and phenotype data sharing. However, for population-based association studies such as GWAS, it has been long recognized that population stratification can seriously confound association results. For large GWAS, it is very likely that there exist population stratification and cryptic relatedness, which will result in inflated Type I error in association testing. Although many methods have been developed to control for population stratification, only two of these approaches can be used to control population stratification without individual-level data: one is based on genomic control (GC) and the other one is based on linkage disequilibrium score regression (LDSC). However, the performance of these two approaches is currently unknown. In this study, we use extensive simulation studies including populations with subpopulations, spatially structured populations, and populations with cryptic relatedness to compare the performance of these two approaches to control for population stratification using only GWAS summary statistics without individual-level data. Data sets from the genetic analysis workshop 19 and UK Biobank are also used to evaluate these two approaches. We demonstrate that the intercept of LDSC can be used as a more accurate correction factor than GC. The results from this study will provide very useful information for researchers using GWAS summary statistics while trying to control for population stratification.