  The unimodular theory of gravity is an alternative perspective to traditional
Einstein's general relativity and opens new possibilities for exploring its
implications in cosmology. In this paper, we investigate the unimodular gravity
(UG) with the latest cosmological data from the Pantheon sample of Type Ia
supernovae (SN), Baryon Acoustic Oscillations (BAO), and the observational H(z)
data from Differential Age method (DA). We consider a model consisting of a
generalized cosmological constant with radiation and dark matter. The
considered theory respects only unimodular coordinate transformations. We fit
our model with low-redshift data from SN and DA and determine the value of
parameter $\xi$ of the theory. We find the best-fit value of parameter $\xi
=6.23 \pm 0.5$; which deviates from 6, for which the theory becomes the
standard general theory of relativity. We further study the Hubble constant
problem by combining the SN and DA data with BAO data. We observe deviation in
the value of $H_0$ from the standard $\Lambda$CDM model. We obtain $H_0$ as
$70.7 \pm 4.1 \ \mbox{Km s}^{-1} \mbox{Mpc} ^{-1}$ and $69.24 \pm 0.90 \
\mbox{Km s}^{-1} \mbox{Mpc} ^{-1}$ from supernovae data and BAO data,
respectively in unimodular gravity. Combining the BAO data with SN+DA data set,
we obtain $H_0$ as $70.57 \pm 0.56 \ \mbox{Km s}^{-1} \mbox{Mpc} ^{-1}$.
