The instantaneous luminosity of the LHC will increase up to a factor of seven with respect to the original design value to explore physics at higher energy scale. The inner station of the ATLAS muon end-cap system (Small Wheel) will be replaced by the New Small Wheel (NSW) to benefit from the high luminosity. The NSW will provide precise track-segment information to the Level-1 trigger system in order to suppress the trigger rate from fake muon tracks. This article summarizes the NSW trigger decision system and track-segment finding algorithm implemented in the trigger processor, and discusses results of performance studies on the trigger system. The
results demonstrate that the NSW trigger system is capable of working with good performance satisfying the requirements.