  We present the model of transit universe from early deceleration phase to
current acceleration phase under the framework of general relativity in
presence of gravitational coupling $G(t)$ and cosmological terms $\Lambda(t)$.
The Einstein's field equations have been solved by considering time dependent
deceleration parameter (DP) which renders the scale factor $a =
(t^{n}e^{kt})^{\frac{1}{m}}$ where $m$, $n$ and $k$ are positive constants. The
cosmological term $(\Lambda(t))$ is found to be positive and a decreasing
function of time which supports the result obtained from supernovae Ia
observations. The geometrical and kinematical features of the model are
examined in detail.
