A level set-based method was introduced to design the metamaterials which can exhibit negative Poisson's ratio and negative thermal expansion simultaneously.Negative Poisson's ratio (also called auxeticity) and negative thermal expansion are phenomena that may rarely be found in the nature materials.It is now known that these unusual properties are mainly dependent on the particular features in the material's micro-or nano-structural deformation when subjected to a thermal or mechanical load.A numerical homogenization method was applied to evaluate the effective properties of the microstructure,and the multi-phase level set method was used to implement the shape and topology evolutions of the microstructure.Two numerical examples were given to demonstrate the feasibility of the proposed topology optimization method,which provides a systematic design method for the design of artificial materials with special properties.