In Thomson scattering (TS) diagnostic system, the stray light greatly affects the signal-to-noise ratio (SNR). The suppression issue is particularly severe for the low density and low temperature plasma due to very few scattered photons and narrow line broadening. The traditional methods, such as Brewster window, beam dump and transmission pipe with black-coated internal surface, have been adopted in the stray light suppression system on our Linear Magnetized Plasma (LMP) device. Moreover, an assembly of tapered apertures are placed in the optical path. Via numerical simulation, the optimal configuration of the adjustable aperture tube (size, location, and orientation) that provide the best suppression has been found. Numerical results show that the optimal aperture group with 6 mm and 8 mm tapered apertures can maintain over 97% transmission rate of the main laser energy while reducing stray light by 99.6%.