This paper is to investigate the existence of β- convergence and σ- convergence for financial institutional characteristics for the dataset of 102 countries from 1980 to 2009. The research is based on panel data econometric models and 10 financial depth indicators. The partial effects of corruption and financial openness are also to be estimated. The main conclusion is that the world exhibits steady financial development as well as β-convergence of financial depth indicators, the middle income countries converging relatively faster. Nevertheless the speed of convergence is not sufficient for the developing world to catch up quickly.