  We present an estimate of the occurrence rate of hot Jupiters ($7\
R_{\oplus}\leq R_{p}\leq 2\ R_{J}$, $0.8 \leq P_{b}\leq 10$ days) around
early-type M dwarfs based on stars observed by TESS during its Primary Mission.
We adopt stellar parameters from the TESS Input Catalog, and construct a sample
of 60,819 M dwarfs with $10.5 \leq T_{\rm mag}\leq 13.5$, effective temperature
$2900 \leq T_{\rm eff}\leq 4000\ K$ and stellar mass $0.45\leq M_{\ast}\leq
0.65\ M_{\odot}$. We conduct a uninformed transit search using a detection
pipeline based on the box least square search and characterize the searching
completeness through an injection and recovery experiment. We combine a series
of vetting steps including light centroid measurement, odd/even and secondary
eclipse analysis, rotation and transit period synchronization tests as well as
inspecting the ground-based photometric, spectroscopic and imaging
observations. Finally, we find a total of nine planet candidates, all of which
are known TESS objects of interest. We obtain an occurrence rate of
$0.27\pm0.09\%$ for hot Jupiters around early-type M dwarfs that satisfy our
selection criteria. Compared with previous studies, the occurrence rate of hot
Jupiters around early-type M dwarfs is smaller than all measurements for FGK
stars, although they are consistent within 1--2$\sigma$. Combining results from
transit, radial velocity and microlensing surveys, we find that hot Jupiters
around early-type M dwarfs possibly show a steeper decrease in occurrence rate
per logarithmic semi-major axis bin (${{\rm d}N}/{\rm d}\log_{10} a$) when
compared with FGK stars.
