Considering the non-conservation of the matter content of the universe, a cosmological model has been built up, on the basis of an assumption of an inter-conversion between matter and the dark energy. A function of time has been introduced to represents the phenomenon of non-conservation of the matter content. By definition, this function is proportional to the matter content of the universe at any point of time. Time dependence of this function has been determined from Brans-Dicke field equations. The monotonically decreasing nature of this function indicates a continuous conversion of matter into dark energy. Time variations of the proportions of matter and dark energy contents of the universe have been derived in terms of this function. To find the time evolution of various cosmological quantities, an empirical scale factor has been used in the present model. This scale factor has been selected in a way such that it generates a deceleration parameter which shows a change of sign with time, implying a change of phase of the expanding universe from deceleration to acceleration. Dependence of the scalar field upon the scale factor has also been chosen empirically. Time variations of several quantities of cosmological interest have been shown graphically.