Spike sorting, which classifies spiking events of different neurons from single electrode recordings, is an essential and widely used step in neural data processing and analysis. The recent development of brain-machine interfaces enables online control of external devices and closed-loop neuroprosthetics using single-unit activity, making online spike sorting desired. Most existing spike sorters work in an offline manner, i.e., sorting after data collection. However, offline spike sorters usually suffer from performance degradation in online tasks due to the instability of neural signals. In an online process, neuronal properties can change over time (such as waveform deformations), and new neurons can appear. Therefore, a static spike sorter requires periodic recalibration to maintain its performance. This study proposes a novel online spike sorter based on neuromorphic models (NeuSort), which can adaptively adjust itself to cope with changes in neural signals. NeuSort can robustly track individual neurons' activities against waveform deformations and automatically recognize new coming neurons in real-time. The adaptation ability of NeuSort is achieved by online parameter updates of the neuromorphic model, according to the plasticity learning rule inspired by biological neural systems. Experimental results on both synthetic and neural signal datasets demonstrate that NeuSort can classify spiking events automatically and cope with non-stationary situations in neural signals. NeuSort also provides ultra-low energy cost computation with neuromorphic chips.