In this paper, we propose a weighted multiple classifier framework based on random projections. Similar to the mechanism of other homogeneous ensemble methods, the base classifiers in our approach are obtained by a learning algorithm on different training sets generated by projecting the original up-space training set to lower dimensional down-spaces. We then apply a Least SquarE−based method to weigh the outputs of the base classifiers so that the contribution of each classifier to the final combined prediction is different. We choose Decision Tree as the learning algorithm in the proposed framework and conduct experiments on a number of real and synthetic datasets. The experimental results indicate that our framework is better than many of the benchmark algorithms, including three homogeneous ensemble methods (Bagging, RotBoost, and Random Subspace), several well-known algorithms (Decision Tree, Random Neural Network, Linear Discriminative Analysis, K Nearest Neighbor, L2-loss Linear Support Vector Machine, and Discriminative Restricted Boltzmann Machine), and random projection-based ensembles with fixed combining rules with regard to both classification error rates and F1 scores.