  We study the recently discovered Be/X-ray pulsar MAXI J0655--013 using the
2022 \emph{NuSTAR} observations. The paper is the first detailed study of the
timing and spectral properties of the source. The pulse profiles of the pulsar
vary with energy. The pulsed fraction is found to increase monotonically with
energy. In between the two \emph{NuSTAR} observations, a large spin-up rate of
$\sim$ -1.23 s d$^{-1}$ is observed, which can be due to large spin-up torque
acting on the pulsar during an outburst. Such a large spin-up rate is observed
for the first time in an X-ray pulsar during an outburst. The variation of the
spin period with time can be employed to obtain the orbital parameters of the
binary system, and we found the orbital period to be $\sim$ 27.9 d. The second
\emph{NuSTAR} observation is done in a low luminosity state ($L_{X}
\sim$3.9$\times$10$^{34}$ \unilum). We have detected the pulsation of the
pulsar in such a low luminosity state. In such a low luminosity state, the
pulsar MAXI J0655--013 might be accreting from the cold disk.
