Steganography in low bit-rate speech streams is an important branch of Voice-over-Internet Protocol steganography. From the point of preventing cybercrimes, it is significant to design effective steganalysis methods. In this paper, we present a support-vector-machine-based steganalysis of low bit-rate speech exploiting statistic characteristics of pulse positions. Specifically, we utilize the probability distribution of pulse positions as a long-time distribution feature, extract Markov transition probabilities of pulse positions according to the short-time invariance characteristic of speech signals, and employ joint probability matrices to characterize the pulse-to-pulse correlation. We evaluate the performance of the proposed method with a large number of G.729a-encoded speech samples and compare it with the state-of-the-art methods. The experimental results demonstrate that our method significantly outperforms the previous ones on detection accuracy, false positive rate, and false negative rate at any given embedding rates or with any sample lengths. Particularly, this method can successfully detect steganography employing only one or a few of the potential cover bits, which is hard to be effectively detected by the existing methods.