As an effective ensemble learning algorithm for classification and regression tasks， the random forest （RF） also faces challenges in improving generalization ability and privacy protection. In response to this challenge， this paper proposes an improved Bernoulli-multinomial stacked random forest （BMS-RF） algorithm based on multiple randomness and privacy protection. The basic idea is to introduce Bernoulli distribution Dropout partial feature vectors to select candidate feature vectors in the stage of constructing decision tree splitting features and splitting point selection. By randomly selecting splitting features and splitting points through two polynomial distributions， each decision tree adopts a non numerical query index mechanism to add noise for maintaining its privacy protection mechanism. When integrating classifiers， a multi-layer stack structure is introduced to randomly project the output of the previous layer and concatenate the source training set as new inputs， so that each forest can share the spatial information of the source samples and improve the classification performance of the base learner layer by layer. Theoretical analysis of the consistency and privacy ability of this algorithm shows that BMS-RF can significantly improve classification performance through a stack structure. Experimental results on 14 small and medium-sized datasets verify that the algorithm not only reduces running time but also has better generalization performance. When the privacy protection is strong， it can achieve classification performance similar to RF variants on the basis of simplifying the structure and improving running speed.