Abstract: In the linear logistic discrimination, the dependence structures of various populations are the same. But it is important for theoretical researchs and practical applications that the dependence structures are different in various populations, thus the quadratic discrimination is produced in the paper. The full quadratic logistic discriminant approach has too many parameters to be estimated if the dimensionality, p, is not small, say p>4.An approximation is suggested here which gives a quadratic term in the discriminant function but with a greatly reduced number of parameters. A quasi-Newton iterative computation is used to solve the equations from maximum likelihood estimation. Examples of the prediction of the drought or flood in North China, and in which the number of days when the most high temperature 35℃ in the 1st decade of July in Beijing is less than 2 or not, are provided. Other approximations are suggested in some special cases.