To better evaluate and distribute the middle frequency errors of large telescope, structure function was put forward for such purposes in this paper. Firstly, we carried out a derivation in basic property of the structure function and compared it with traditional root mean square (RMS), which indicates its capability of representing different-scale errors; secondly, conducted an analysis on the statistical property difference of system wavefront under different evaluation scales, which indicates that system error distribution can better follow the normalized distribution under small scale and tend to deviate from the normalized distribution with the scale increase (e.g.: a scale greater than 100 mm); then a method for middle frequency error distribution of large telescope that can simultaneously cover multiple error sources was put forward based on basic property of the structure function; established a conversion relation between the structure function and normalized point source sensitivity (PSSn) put forward by TMT team, and then completed the cross validation among the error distribution indexes and transfer of techniques; finally, carried out an error distribution in primary mirror system of a large telescope based on the method put forward in this paper, which indicates that structure function of the system can meet the requirements under the condition where large-scale RMS is 25nm, roughness is 1nm, middle frequency scale is 250 mm and atmospheric coherent length is 0.4 m (testing environment), and that PSSn=0.9996 obtained from the structure function is greater than PSSn=0.999 5 directly obtained from mirror data can also meet the corresponding requirement.