The dependence of Brans-Dicke (BD) parameter upon the scalar field, for different cosmological era of the expanding universe, has been explored. The time dependence of the scalar field has been determined and thereby the explicit time dependence of the BD parameter has been obtained. Experimental observations regarding the time dependence of the gravitational constant has been considered for this study. The scale factor, Hubble parameter, deceleration parameter, matter density, gravitational constant and the density parameters for matter and dark energy have been expressed in terms of the BD parameter and its time derivatives, showing its role in cosmic expansion. for matter and dark energy. PACS Numbers: 98.80.Jk, 95.30.Sf, 95.30.Ft, 91.10.Op, 95.36.+x