  The model of heavy neutral leptons (HNLs) is one of the well-motivated models
beyond the standard model (BSM) from both theoretical and phenomenological
point of views. It is an indispensable ingredient to explain the puzzle of tiny
neutrino masses and the origin of the matter-antimatter asymmetry in our
Universe, based on the models in which the simplest Type-I seesaw mechanism can
be embedded. The HNL with a mass up to the electroweak scale is an attractive
scenario which can be readily tested in present or near-future experiments
including the LHC. In this work, we study the decay rates of HNLs and find the
sensitive parameter space of the mixing angles between the active neutrinos and
HNLs. Since the mixing between $ \nu_{\tau} $ and HNL is not well established
in literature compared with those of $\nu_e$ and $\nu_{\mu}$ for the HNL of
mass in the electroweak scale, we focus on the channel $ pp\rightarrow
W^{\pm(\ast)} + X\rightarrow \tau^{\pm} N + X$ to search for HNLs at the LHC 14
TeV. The targeted signature consists of three prompt charged leptons, which
include at least two tau leptons. After the signal-background analysis, we
further set sensitivity bounds on the mixing $ |U_{\tau N}|^2 $ with $ M_N $ at
High-Luminosity LHC (HL-LHC). We predict the testable bounds from HL-LHC can be
stronger than the previous LEP constraints and Electroweak Precision Data
(EWPD), especially for $ M_N \lesssim $ 50 GeV can reach down to $ |U_{\tau
N}|^2 \approx 2\times 10^{-6} $.
