This paper presents a method to analyze the Sub Synchronous Oscillation (SSO) problem based on broad learning system (BLS), which can quickly analyze the risk of SSO in a system and take measures. The simulation system is constructed by the eigenvalue analysis method to obtain training data, that solves the problem which is difficult to obtain actual data in SSO problem and makes the model more accurate and the conclusion more convincing. Subsequently, BLS is applied for feature extraction and the prediction model is constructed, the model can show the deep relationship between the oscillation source and topology of the system as well as various operating data, which is difficult to be expressed by formula. The system was tested and validated in the 41-bus system. The feature importance analysis method which comes from eXtreme Gradient Boosting (XGboost) algorithm is proposed and combined with the BLS prediction model, which can analyze the influence of each variable on the prediction results in different series compensation levels, and is validated in the 41-bus system, that makes the results of prediction more interpretable. Finally, the results of simulation show that the model can predict data with high accuracy and give adjustment plans for effective control of the system to avoid the risk of SSO.