Atmospheric scattering directional exponetional function is very important to study of the distribution of skies luminance.The influence of air turbidity factor to atmospheric scattering directional exponetional function was neglected previously.In this paper,influence of air turbidity factor on atmospheric scattering was considered and a scattering function,which proximates clear,cloudy and pseud-overcast by varied turbidity factors,was presented.The atmospheric scattering for varied air condition was considered and molecular scattering was included in the function.Hence it provides a path for further theoretical study on sky luminance distribution.