This study is an effort to depict the spatial and temporal variations in fertility and infant mortality and its determinant within the state with the view that a better understanding of fertility and infant mortality transition taking place in Bihar either when might be possible fertility and infant mortality transition taking place in Bihar. This study begins with the discussion on how is changing in fertility and infant mortality at district level over the period and socio-economic and demographic factors affecting fertility and infant mortality at state level through the combination of statistical analytical tools viz. multiple regression and cox regression. Moreover try to understand that when Bihar will be obtain replacement level of fertility and when will be achieve target of infant mortality according millennium development goal through the analytical tool gompertz model.