  NGC 1042 is a late type bulgeless disk galaxy which hosts a low luminosity
Active Galactic Nuclei (AGN) coincident with a massive nuclear star cluster. In
this paper, we present the integral-field-spectroscopy (IFS) studies of this
galaxy, based on the data obtained with the Mitchell spectrograph on the 2.7
meter Harlan J. Smith telescope. In the central $100\textrm{-}300\ \mathrm{pc}$
region of NGC 1042, we find a circumnuclear ring structure of gas with enhanced
ionization, which we suggest is mainly induced by shocks. Combining with the
harmonic decomposition analysis of the velocity field of the ionized gas, we
propose that the shocked gas is the result of gas inflow driven by the inner
spiral arms. The inflow velocity is $\sim 32\pm10\ \mathrm{km}\
\mathrm{s}^{-1}$ and the estimated mass inflow rate is $\sim 1.1\pm0.3 \times
10^{-3}\ \mathrm{M}_{\odot}\ \mathrm{yr}^{-1}$. The mass inflow rate is about
one hundred times the blackhole's mass accretion rate ($\sim 1.4 \times
10^{-5}\ \mathrm{M}_{\odot}\ \mathrm{ yr}^{-1}$), and slightly larger than the
star formation rate in the nuclear star cluster ($7.94 \times 10^{-4}\
\mathrm{M}_{\odot}\ \mathrm{yr}^{-1}$), implying that the inflow material is
enough to feed both the AGN activity and the star formation in the nuclear star
cluster. Our study highlights that secular evolution can be important in
late-type unbarred galaxies like NGC 1042.
