Optical fiber geometric parameters are an important index that affects optical fiber performance. The gray-scale method is a common method for measuring the geometric parameters of optical fibers. When measuring, it is necessary to illuminate the optical fiber to distinguish the core and the cladding. Since the light is not completely concentrated in the core propagation (part of the light propagates in the cladding), it is difficult to distinguish the interface between the core and the cladding. In order to accurately find the edge of the fiber core, this paper uses two polynomials to fit the light intensity gray distribution of the core and cladding area respectively, and obtains the gray value corresponding to the intersection of the two polynomials as the boundary point between the core and the cladding. So as to get the edge data of the core. The segmented cubic Hermite interpolation is used to correct the measured data, reducing the influence of error points on the fitting. By measuring two sets of fiber end-face images with different imaging qualities, the diameter and out-of-roundness of the fiber core were measured with a standard instrument to be 10.068µm, 0.616%, and 10.397µm, 0.766%. The measured value of the method in this paper is 9.999µm, 0.716% and 10.020µm, 0.857%. Experiments show that the method in this paper has better accuracy and stability for the measurement of optical fiber geometric parameters, and theoretically, the method in this paper has more physical meaning and rationality in the measurement principle than the commonly used gray-scale method.