Super-resolution ultrasound can image microvascular structure and flow at sub-wave-diffraction resolution based on localising and tracking microbubbles. Currently, tracking microbubbles accurately under limited imaging frame rates and high microbubble concentrations remains a challenge, especially under the effect of cardiac pulsatility and in highly curved vessels. In this study, an acceleration-incorporated microbubble motion model is introduced into a Kalman tracking framework. The tracking performance was evaluated using simulated microvasculature with different microbubble motion parameters, concentrations and acquisition frame rates, and in vivo human breast tumour ultrasound datasets. The simulation results show that the acceleration-based method outperformed the non-acceleration-based method at different levels of acceleration and acquisition frame rates and achieved significant improvement in true positive rate (up to 11.3%), false negative rate (up to 13.2%). The proposed method can also reduce errors in vasculature reconstruction via the acceleration-based nonlinear interpolation, compared with linear interpolation (up to 16.7 μm). The tracking results from temporally downsampled low frame rate in vivo datasets from human breast tumours show that the proposed method has better microbubble tracking performance than the baseline method, if using results from the initial high frame data as reference. Finally, the acceleration estimated from tracking results also provides a spatial speed gradient map that may contain extra valuable diagnostic information.