The terahertz (THz) slow-light effect can effectively improve the security and memory property of THz pulse data during transmission. However,the general THz slow-light devices are sensitive to the polarization state changing of the incident THz wave.In this paper,we design a metamaterial structure whose unit cell consists of one cross resonator and four U-shaped resonators.The results show that the THz slow-light effects based on metamaterials are not sensitive to both linear and circularly polarized light. A slow-light effect with the maximum group refractive index of 1 618 is obtained by optimizing parameters of the metamaterial structure.A molybdenum disulfide film between the metamaterial microstructure layer and the SiO2 substrate is embedded.When the carrier concentration of molybdenum disulfide increases from 1.7×1017 cm-3 to 5.1×1019 cm-3,the group refractive index decreases from 1 566 to 26,and a polarization insensitive all-light tunable THz slow-light effect is realized.This study can provides some new ideas for the design of polarization insensitive and all-light tunable THz slow-light devices.