We aim at investigating characteristics of Japan's largest competitive grant Grants-in-Aid for Scientific Research (GASR) system in order to find a desirable research funding system, obtaining more applicants from various academic disciplines, researchers' gender, and ages. Firstly, we briefly describe the Japanese competitive research funding system including the GASR system. Then we investigate the GASR system quantitatively, focusing on its funding, allocation and relationship with the Japanese Science and Technology Basic Plans. Quantitative characteristic analyses are conducted for the GASR system from various perspectives such as type of research projects, academic disciplines, researchers' gender, and ages by investigating the data for applications, acceptances, and budgets allocated in the recent 10 years. Finally, we summarize our findings and conclude the paper by proposing policy recommendations to improve Japan's competitive research funding system.