The High Energy cosmic-Radiation Detection (HERD) facility is a next generation spaceborne detector to be installed onboard the Chinese Space Station for about 10 years. HERD will address major problems in fundamental physics and astrophysics, providing precise measurements of charged-cosmic rays up to PeV energies, performing indirect searches for dark matter in the electron spectrum up to few tens of TeV and monitoring the gamma-ray skymap for surveys and transient searches. HERD is composed of a 3D imaging calorimeter (CALO) surrounded by a scintillating fiber tracker (FIT), a plastic scintillator detector (PSD) and a silicon charge detector (SCD). In addition, a transition radiation detector (TRD) is placed on a lateral side to provide accurate energy calibration. Based on this innovative design, the effective geometric factor of HERD will be one order of magnitud larger than that of current space-based detectors. The HERD trigger strategy is designed to accomplish the scientific goals of the mission, and is based on trigger definitions that rely on the energy deposited in CALO and the PSD. The trigger performances are evaluated using a detailed Monte Carlo simulation that includes the latest HERD geometry. In addition, alternative trigger definitions based on the event topology can be established thanks to the photodiode readout of CALO crystals. The feasibility of these topological triggers is also investigated and presented. © Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0)