The lens surface figure precision of lithography objective lens is a key factor which influences the system imaging quality. In order to meet lens surface figure accuracy RMS better than 1~2 nm, this article introduces a lens support structure with multi point equal supporting which wholly has the radical freedom. Then, based on gravity deformation and thermal deformation, the structure optimization is finished. Finally, due to gravity and thermal load, the finite element analysis of lens deformation is done. Results are as follows: lens surface figure RMS of the upper surface causing by gravity is 0.429 nm, while the lower surface is 0.294 nm, and lens surface figure RMS of the upper surface causing by thermal load is 0.409 nm, while the lower surface is 0.063 nm. The results indicate that the lens supporting structure is of high precision, and can be satisfied with the lithography objective lens surface accuracy.