In the speaker verification task based on Gaussian Mixture Model-Universal Background Model (GMM-UBM), by constructing the UBM as a tree structure, the kernel Gaussians suitable for different speakers can be quickly selected, which speeds up the modeling of speaker acoustic space by GMM. The tree-based kernel selection algorithm (TBKS) introduces a beam-width, which increases the candidate range of kernels and improves the kernel selection accuracy. In this paper, we improve the TBKS algorithm by introducing a recall rate to adjust the number of nodes recalled in each layer of the tree structure. This adjustment refines the quantity and resolution of Gaussian distributions in various subspaces within the acoustic space, compensating for the loss caused by discarding some significant Gaussians erroneously. Speaker verification experiments are carried out based on the Aishell2 dataset. The results reveal that the modified TBKS algorithm reduces EER by 7.5% relatively and increses computational reduction factor to 42.93, enhancing both recognition accuracy and speed. In addition, the test speech is spliced into different lengths and common environmental noise is added to verify the universality of the improved algorithm.