Phasor measurement units (PMUs) can provide real-time measurement data to construct the ubiquitous electric of the Internet of Things. However, due to complex factors on site, PMU data can be easily compromised by interference or synchronization jitter. It will lead to various levels of PMU data quality issues, which can directly affect the PMU-based application and even threaten the safety of power systems. In order to improve the PMU data quality, a data-driven PMU bad data detection algorithm based on spectral clustering using single PMU data is proposed in this paper. The proposed algorithm does not require the system topology and parameters. Firstly, a data identification method based on a decision tree is proposed to distinguish event data and bad data by using the slope feature of each data. Then, a bad data detection method based on spectral clustering is developed. By analyzing the weighted relationships among all the data, this method can detect the bad data with a small deviation. Simulations and results of field recording data test illustrate that this data-driven method can achieve bad data identification and detection effectively. This technique can improve PMU data quality to guarantee its applications in the power systems.