Thermal-induced two-phase flow instabilities could badly slow the runtime performance of two-phase systems, such as boiling water reactor core, and even endanger the safe operation. Hence, many researchers have carried out numerous researches on flow instability characteristics, but few publications cover the effects of local throttling on two-phase flow instabilities in open-channel systems such as coolant rod bundle subchannel with spacer grids in the nuclear reactor core. This paper provides a numerical study on the effects of local throttling on two-phase flow instabilities in a simplified typical coolant open-channel system in a nuclear reactor core by using the NUSOL-SYS code. The effects of local throttling ratio, throttling position, and other throttling parameters on the stability of the boiling channel system were carried out. The results show that usually in uniformly distributed throttling conditions, the stability of the system and high throttling ratio are positively correlated. In fixed throttle ratio conditions, the stability of the system is positively correlated with the distance from the throttling region to the entrance and local void fraction. If throttling regions are uniformly arranged along the heating channel with a certain value, the number of throttle regions will enhance the instability of the system. Besides, this paper preliminarily proposed a criterion function f(n, RT, α) to study the complicated throttling effects on flow instability which could provide technical reference for the safe design and operation of two-phase systems, especially, the reactor core.