Accurate estimation of the traffic state can help to address the issue of urban traffic congestion, providing guiding advices for people's travel and traffic regulation. In this paper, we propose a novel short-term traffic flow prediction algorithm based on an adaptive multi-kernel support vector machine (AMSVM) with spatial-temporal correlation, which is named as AMSVM-STC. First, we explore both the nonlinearity and randomness of the traffic flow, and hybridize Gaussian kernel and polynomial kernel to constitute the AMSVM. Second, we optimize the parameters of AMSVM with the adaptive particle swarm optimization algorithm, and propose a novel method to make the hybrid kernel's weight adjust adaptively according to the change tendency of real-time traffic flow. Third, we incorporate the spatial-temporal correlation information with AMSVM to predict the short-term traffic flow. We evaluate our algorithm by doing thorough experiment on real data sets. The results demonstrate that our algorithm can do a timely and adaptive prediction even in the rush hour when the traffic conditions change rapidly. At the same time, the proposed AMSVM-STC outperforms the existing methods.