An approach to the acceleration of parametric weak classifier boosting is proposed. Weak classifier is called parametric if it has fixed number of parameters and, therefore, can be represented as a point in multidimensional space. Genetic algorithm is used to learn parameters of such classifier. Proposed approach also takes cases when effective algorithm for learning some of the classifier parameters exists into account. Experiments confirm that such an approach can dramatically decrease classifier training time while keeping both training and test errors small, at least for some widely used pattern recognition algorithms.