It is important and urgent to develop microwave low frequency band-pass and high frequency band-stop composite structures according to the needs of marine environment stealth weapons and equipment constructions. In this paper, a hollow hexagonal periodic structure is originally designed and the microwave band-pass and band-stop characteristics are investigated through the CST software simulation. As an optimization result, the numerical periodic structure parameters of hexagon ring are as follows: hexagon ring side length is 2.7 mm, line width 0.5 mm and gap width 0.15 mm, which shows a transmission of 83% at 0-2 GHz, and meanwhile a shielding efficiency of more than 10 dB at 8-18 GHz, thereby basically justifying our design target. On this basis, a new type of double-layers' composite frequency selective surface (FSS) structure which is composed of facial layer, hollow hexagon ring array 1, middle spacer layer, hollow hexagon ring array 2 and another facial layer stacked layer by layer, is creatively designed, which displays excellent microwave low frequency band-pass and high frequency band-stop performances compared with a single layer hollow hexagonal periodic structure, and by simulation and optimization, structural parameters of the upper FSS structure are as follows: hexagon ring side length is 3.0 mm, line width 0.5 mm, gap width 0.4 mm, and the lower FSS structure parameters are as follows: hexagon ring side length is 3.2 mm, line width 0.5 mm, gap width 1.0 mm; simulation results show itself that dual different layers' FSS design presents itself excellent low frequency band-pass and high frequency band-stop transformation characteristics, and the fast switch capacity is the basic foundation for both excellent low frequency band-pass and outstanding high frequency band-stop characteristics. The effects of wave incidence angle (TE) on electrical performance of dual-layers FSS are investigated and the results indicate that the designed dual-layers' FSS possesses a wide angle insensitivity in a range of 0-45°, which is especially beneficial to engineering applications. Finally the composite structures with dual-layers' FSSs are manufactured and verified, and high transmission up to 95.6% at 0-2 GHz frequency band and more than 10 dB shielding efficiency at 7.05-18 GHz are obtained, which strongly testifies our design idea and has important significance for developing the high performance band-pass and band-stop composite structure and new electromagnetic functional composite materials.