Extreme　ultraviolet(EUV)lithography　with　high　numerical　aperture(NA)is　a　future　technology　to　manufacture　the　integ-rated　circuit　in　sub-nanometer　dimension.Meanwhile,source　mask　co-optimization(SMO)is　an　extensively　used　ap-proach　for　advanced　lithography　process　beyond　28　nm　technology　node.This　work　proposes　a　novel　SMO　method　to　improve　the　image　fidelity　of　high-NA　EUV　lithography　system.A　fast　high-NA　EUV　lithography　imaging　model　is　estab-lished　first,which　includes　the　effects　of　mask　three-dimensional　structure　and　anamorphic　magnification.Then,this　pa-per　develops　an　efficient　SMO　method　that　combines　the　gradient-based　mask　optimization　algorithm　and　the　compress-ive-sensing-based　source　optimization　algorithm.A　mask　rule　check(MRC)process　is　further　proposed　to　simplify　the　optimized　mask　pattern.Results　illustrate　that　the　proposed　SMO　method　can　significantly　reduce　the　lithography　pat-terning　error,and　maintain　high　computational　efficiency.