  The High Energy X-ray telescope (HE) on-board the Hard X-ray Modulation
Telescope (\textit{Insight}-HXMT) can serve as a wide Field of View (FOV)
gamma-ray monitor with high time resolution ($\mu$s) and large effective area
(up to thousands cm$^2$). We developed a pipeline to search for Gamma-Ray
Bursts (GRBs), using the traditional signal-to-noise ratio (SNR) method for
blind search and the coherent search method for targeted search. By taking into
account the location and spectrum of the burst and the detector response, the
targeted coherent search is more powerful to unveil weak and sub-threshold
bursts, especially those in temporal coincidence with Gravitational Wave (GW)
events. Based on the original method in literature, we further improved the
coherent search to filter out false triggers caused by spikes in light curves,
which are commonly seen in gamma-ray instruments (e.g. \textit{Fermi}/GBM,
\textit{POLAR}). We show that our improved targeted coherent search method
could eliminate almost all false triggers caused by spikes. Based on the first
two years of \textit{Insight}-HXMT/HE data, our targeted search recovered 40
GRBs, which were detected by either \textit{Swift}/BAT or \textit{Fermi}/GBM
but too weak to be found in our blind search. With this coherent search
pipeline, the GRB detection sensitivity of \textit{Insight}-HXMT/HE is
increased to about 1.5E-08 erg/cm$^2$ (200 keV$-$3 MeV). We also used this
targeted coherent method to search \textit{Insight}-HXMT/HE data for
electromagnetic (EM) counterparts of LIGO-Virgo GW events (including O2 and O3a
runs). However, we did not find any significant burst associated with GW
events.
