With the rapid development of the inverter-based generation, the synchronization instability of Grid-following converter (GFL) is one of the main issues for the modern power system operation. Due to the high-order and nonlinear characteristics of the GFL model, traditional stability analysis methods, e.g., phase portrait, equal-area criterion, fall to achieve a perfect synchronization stability assessment. Machine Learning method has widely used in the frequency and voltage stability assessment for the power system and present advantages on fast-computation and high-accuracy. Based on this concept, this paper is the first to use the machine learning for the synchronization stability assessment of the GFL and moreover, to propose a Fuzzy C-Means and Sparrow Search Algorithm optimization for Deep Belief Network (FCM-SSA-DBN) methods to classify the synchronization stability into different levels. The Matlab simulation serves to prove that the machine learning method has nearly 100^% accuracy on the stability assessment and up-to 98.9% accuracy on the stability classification.