In this work, we study a cosmological model of spatially homogeneous and isotropic accelerating universe which exhibits a transition from deceleration to acceleration. For this, Friedmann Robertson Walker(FRW) metric is taken and Hybrid expansion law $a(t)=t^{alpha} exp(beta t )$ is proposed and derived. We consider the universe to be filled with two types of fluids barotropic and dark energy which have variable equations of state. The evolution of dark energy, Hubble, and deceleration parameters etc., have been described in the form of tables and figures. We consider $581$ datas of observed values of distance modulus of various SNe Ia type supernovae from union $2.1$ compilation to compare our theoretical results with observations and found that model satisfies current observational constraints. We have also calculated the time and redshift at which acceleration in the Universe had commenced.
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