As a typical form of optical fringes with a quadratic phase, Newton's ring patterns play an important role in spherical measurements and optical interferometry. A variety of methods have been used to analyze Newton's ring patterns. However, it is still rather challenging to fulfill the analysis. We present a deep-learning-based method to estimate the parameters of Newton's ring patterns and fulfill the analysis accordingly. The experimental results indicate the excellent accuracy, noise robustness, and demodulation efficiency of our method. It provides another applicable approach to analyzing Newton's ring patterns and brings insights into fringe analysis and interferometry-based measurements.