With the wide application of global positioning system (GPS), more and more electric bicycles are equipped with GPS sensors. Massive trajectory data recorded by those sensors are of great value in many fields, such as users’ travel patterns analysis, decision support for urban planners, and so on. However, the low-cost GPS sensors widely used on electric bicycles cannot provide high-precision positioning. Besides, the map matching for the electric bicycles’ track data is more complex and challenging due to: (1) many stay points on electric bicycles’ trajectories; (2) higher sampling frequency and shorter distance between adjacent track points on electric bicycle’s track data; (3) some roads only open for electric bicycles, and the accuracy of matching is sensitive to the quality of the road network. To solve those issues mentioned above, an adaptive and accurate road network map matching algorithm is proposed named KFTS-AMM, which consists of two main components: the segmented Kalman filtering based trajectory simplification (KFTS) algorithm and segmented hidden Markov model based adaptive map matching (AMM) algorithm. Since Kalman filtering algorithm can be used for optimal state estimation, the trajectory simplification algorithm KFTS can make the trajectory curve smoother and reduce the impact of abnormal points on the accuracy of map matching by fixing the trajectory points automatically in the process of trajectory simplification. Besides, the matching algorithm AMM is used to reduce the impact of invalid trajectory segments on the map matching accuracy. Moreover, stay points identification and merging step are added into the processing of track data, and the accuracy is further improved. Extensive experiments conducted on the real-world track dataset of electric bicycles in Zhengzhou city show that the proposed approach KFTS-AMM outperforms baselines in terms of accuracy and can speed up the matching process by using the simplified track data significantly.