  This paper is devoted to investigate the anisotropic locally rotationally
symmetric (LRS) Bianchi type-I space-time in the context of the recently
proposed $f(Q)$ gravity in which $Q$ is the non-metricity scalar. For this
purpose, we consider a linear form of $f\left( Q\right) $ gravity model,
specifically, $f\left( Q\right) =\alpha Q+\beta $, where $\alpha $ and $% \beta
$ are free parameters and we analyzed the exact solutions of LRS Bianchi type-I
space-time. The modified Friedmann equations are solved by presuming an
expansion scalar $\theta \left( t\right) $ is proportional to the shear scalar
$\sigma \left( t\right) $ which leads to the relation between the metric
potentials as $A=B^{n}$ where $n$ is an arbitrary constant. Then we constrain
our model parameters with the observational Hubble datasets of 57 data points.
Moreover, we discuss the physical behavior of cosmological parameters such as
energy density, pressure, EoS parameter, and deceleration parameter. The
behavior of the deceleration parameter predicts a transition from deceleration
to accelerated phases in an expanding Universe. Finally, the EoS parameter
indicates that the anisotropic fluid behaves like the standard $\Lambda $CDM
model.
