Trigger process for initial breakdown between trigger and cathode is important to the performance of three-electrode gas spark gaps. However

it was experimentally observed that breakdown nearly coinstantaneously formed between trigger-cathode and trigger-anode in some three-electrode gas spark gaps by the help of high speed camera. Hence

we established a simulation model for the trigger process in the experimental three-electrode gas spark gap by PIC-MCC code

Moreover

we obtained the temporal and spatial density distribution evolution of electrons and ions

explained the mechanism of forming plasma channel between trigger and cathode（or anode）

and analyzed the influences of electric field distribution and charge accumulation on trigger process. It is revealed that the secondary electron emission on the insulator is the main factor to the breakdown coinstantaneously formed between trigger-cathode and trigger-anode in three-electrode gas spark gaps. It will be helpful to further optimize the performances of three-electrode gas spark gaps.