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.