  The present study deals with spatially homogeneous and totally anisotropic
locally rotationally symmetric (LRS) Bianchi type I cosmological model with
variable $G$ and $\Lambda$ in presence of imperfect fluid. To get the
deterministic model of Universe, we assume that the expansion $(\theta)$ in the
model is proportional to shear $(\sigma)$. This condition leads to $A=\ell
B^{n}$, where $A$,\;$B$ are metric potential. The cosmological constant
$\Lambda$ is found to be decreasing function of time and it approaches a small
positive value at late time which is supported by recent Supernovae Ia (SN Ia)
observations. Also it is evident that the distance modulus curve of derived
model matches with observations perfectly.
