The development of the optical system of the off-axial three-mirror-anastigmat (TMA) has been restricted for a long time by the current design level

and the difficulties in manufacture and test. In this paper

an improved design of the off-axial TMA optical system is proposed

with a new optical structure

and two design examples are provided. The optical elements of the TMA system are reasonably arranged

the secondary mirror is designed as spherical surface

and the primary and the third mirror are optimized with high-order aspheric coefficients. The MTF curve of the designed system approaches that of the optical diffraction limit

with an improved value of 0.6 at the spatial frequency of 50pl/mm. Compared with the normal off-axial TMA optical system

the Strehl ratio can be elevated from 0.91 to 0.93. The surface tolerance is relaxed from λ/50 to λ/40

and the assembling tolerance of the primary mirror

the second mirror and the third mirror can be relaxed by a factor of 4. The improved design makes the manufacture and the assembly of the mirrors of the off-axial TMA optical system much easier

and helps to achieve excellent performance of the system in the level of optical diffraction limit. These are beneficial to the popularization of the off-axial TMA optical system.