This paper explores the relationship between board compositions/structures and operating performances of financial institutions listed on the Taiwan Stock Exchange and the Taipei Stock Exchange in 1996-2017. Return on assets and return on equity are referred to as the proxy variable for operating performances in the regression analysis on the influence of board compositions. The empirical results indicate no significant effects of the combined CEO and chairperson roles, board size, the deviation between control and cash flows on operating performances of financial institutions. In fact, a higher percentage of ownership by board directors and supervisors is beneficial to return on equity. The percentage of collateralized shares by directors and supervisors exhibits significant and negative influence on return on assets and return on equity. The increase in the number of independent directors reports a significant and positive effect on return on assets and return on equity. Finally, the combined role of directors and managers has adverse effects on return on assets.