The Insight-Hard X-ray Modulation Telescope (Insight-HXMT) is a broadband X-ray and gamma-ray (1-3000 keV) astronomy satellite. One of its three main telescopes is the High Energy X-ray telescope (HE). The main detector plane of HE comprises 18 NaI(Tl)/CsI(Na) phoswich detectors, where NaI(Tl) is used as the primary detector to measure similar to 20-250 keV photons incident from the field of view (FOV) defined by collimators, and CsI(Na) is used as the active shielding detector to NaI(Tl) by pulse shape discrimination. Additionally, CsI(Na) is used as an omnidirectional gamma-ray monitor. The HE collimators have a diverse FOV, i.e. 1.1 degrees x5.7 degrees (15 units), 5.7 degrees x5.7 degrees (2 units), and blocked (1 unit). Therefore, the combined FOV of HE is approximately 5.7 degrees x5.7 degrees. Each HE detector has a diameter of 190 mm resulting in a total geometrical area of approximately 5100 cm(2), and the energy resolution is similar to is an element of 15% at 60 keV. For each recorded X-ray event by HE, the timing accuracy is less than 10 mu s and the dead-time is less than 10 mu s. HE is used for observing spectra and temporal variability of X-ray sources in the 20-250 keV band either by pointing observations for known sources or scanning observations to unveil new sources. Additionally, HE is used for monitoring the gamma-ray burst in 0.2-3 MeV band. This paper not only presents the design and performance of HE instruments but also reports results of the on-ground calibration experiments.