The mechanical and thermal properties of graphene kirigami are strongly dependent on the tailoring structures. Here, thermal conductivity of three typical graphene kirigami structures, including square kirigami graphene, reentrant hexagonal honeycomb structure, and quadrilateral star structure under uniaxial strain are explored using molecular dynamics simulations. We find that the structural deformation of graphene kirigami is sensitive to its tailoring geometry. It influences thermal conductivity of graphene by changing heat flux scattering, heat path, and cross-section area. It is found that the factor of cross-section area can lead to four times difference of thermal conductivity in the large deformation system. Our results are elucidated based on analysis of micro-heat flux, geometry deformation, and atomic lattice deformation. These insights enable us to design of more efficient thermal management devices with elaborated graphene kirigami materials.