An approximate method of computing the misclassification probabilities for quadratic discriminant functions (QDF) with known covariance matrices is suggested in this paper. Large scale simulation from empirical distribution of experimental data is used to test the effectivenessof the approximation and compare its performance against an existing method. It is shown that thisapproximation method performs well for multivariate normal distributions of dimension 2, 3. 4, 5,7, and 10. Exact expressions for computing these probabilities for univariate quadratic discriminant function are provided.