Large-scale simultaneous hypothesis testing problems are ubiquitous in many sci entific fields including genomic and image analysis.Many methods have been devel oped for controlling false discovery rate (FDR) to address multiple testing problems.How-ever, most available approaches focus on the accurate estimation of FDR and only a few approaches deal with the power of the testing rules subject to controlling FDR.In this paper, we intend to optimize the power of the test when controlling FDR at the pre-speci?ed level.To achieve this objective, we derive a theorem on the limit of FDR as the number of hypotheses tends to in?nity.Based on the theorem, we propose a new concept, asymptotic FDR, which is close to FDR.aFDR has a clear advantage over traditional FDR in that it has a relative simple expression making it possible to study aFDR thoroughly.Our new approach reveals an important fact that under some settings not all values of FDR can be controlled, an issue which has not been addressed in the literature to the best of our knowledge.Consequently the concept of plausible controlling values" of FDR is introduced.A practical procedure for constructing a testing rule with maximum power and speci?c controlling FDR is developed.We show through simulations that the new approach has the correct con trolling FDR and yields higher power compared to other existing methods in most cases of interest.