Steganalysis of adaptive multi-rate (AMR) speech is a hot topic for controlling cybercrimes grounded in steganography in related speech streams. In this paper, we first present a novel AMR steganalysis model, which utilizes extreme gradient boosting (XGBoost) as the classifier, instead of support vector machines (SVM) adopted in the previous schemes. Compared with the SVM-based model, this new model can facilitate the excavation of potential information from the high-dimensional features and can avoid overfitting. Moreover, to further strengthen the preceding features based on the statistical characteristics of pulse pairs, we present the convergence feature based on the Markov chain to reflect the global characterization of pulse pairs, which is essentially the final state of the Markov transition matrix. Combining the convergence feature with the preceding features, we propose an XGBoost-based steganalysis scheme for AMR speech streams. Finally, we conducted a series of experiments to assess our presented scheme and compared it with previous schemes. The experimental results demonstrate that the proposed scheme is feasible, and can provide better performance in terms of detecting the existing steganography methods based on AMR speech streams.