  In this article, we have discussed the results of our investigation. We
consider an anisotropic viscous cosmological model of (LRS) Bianchi type I
spacetime universe filled with a viscous fluid under $f(Q)$ gravity. We have
studied the modified $f(Q)$ gravity with quadratic form $f(Q)=\alpha
Q^{2}+\beta$, where $Q$ is called as a non-metricity scalar and $\alpha $,
$\beta$ are positive constants. We obtain the modified Einstein field equation
by considering the viscosity coefficient $\xi(t)=\xi_{0}H$ and obtained the
scale factor $a(t)=2~sinh\left (\frac{m+ 2}
{6}\sqrt{\frac{\xi_{0}}{\alpha(2m+1)}}t\right)$.We applied the observational
constraint on the apparent magnitude $m(z)$ using the $\chi^{2}$ test formula
with observational data set like JLA or Union 2.1 compilation and obtained the
best approximate values of the model parameters ${ m,\alpha, H_{0} \xi_{0}}$.
We have analyzed our model and found a transit phase quintessence anisotropic
accelerating universe. We also examined the bulk viscosity equation of state
(EoS) parameter $\omega_{v}$ and obtained its current value as
$\omega_{v}<-1/3$, which shows the dark energy dominant model, cosmological
constant, phantom, and super-phantom dark energy models, and tends to the
$\Lambda$CDM value ($\omega_{v}=-1$) in the late time. We also estimate the
current age of the universe as $t_{0}\approx13.6$ Grys and analyze the
Statefinder parameters with $(s,r)\to(0,1)$ as $t \to \infty$.
