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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$σ$. 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.