  In this paper, we report on the hard X-ray observation of the X-ray pulsar 1E
1145.1-6141 performed with the Nuclear Spectroscopic Telescope Array mission
(NuSTAR). The coherent pulsation of the source with a period of
$\sim296.653\;\pm\;0.021\;s $ is detected. The source may be in the equilibrium
phase, according to the most recent measurements of its pulse period. The pulse
profile reveals a mild energy dependence and generally hints at a pencil-beam
pattern. The pulse profile have evolved with time. The Pulse fraction is found
to depend on energy with a fall in the value at $\sim 32\; keV$. The NuSTAR
spectra can be approximated by a composite model with two continuum components,
a blackbody emission, cut-off powerlaw, and a discrete component in the form of
gaussian to account for the emission line of iron. The estimated absorbed flux
of the source is $\sim6\times10^{-10}\;erg\;cm^{-2}\;s^{-1}$ which corresponds
to a luminosity of $\sim5\times 10^{36}\;erg\;s^{-1}$. Pulse phase-resolved
spectroscopy were performed to understand the evolution of spectral parameters
with pulse phase. The estimated blackbody radius is found to be consistent with
the size of the theoretical prediction.
