By taking the single checkerboard image of fisheye cameras to characterize as targets and comprehensively using multiple geometric constraints, the initial values of fisheye camera parameters are solved in different steps and the global optimization is simultaneously implemented. The exact principal point location (u0, v0) of the camera is obtained by means of fisheye image contours and their symmetry, in which the difficulty in detecting contour points under a black background is skillfully avoided through scanning the bounding box of fisheye image contours. Two group of projection ellipses on the fisheye checkerboard images are accurately fitted whose intersection points are back-projected to the unit sphere to obtain vanishing points of the parallel lines, and the initial value (fx, fy) of the equivalent focal length of camera and the initial angle of rotation matrix are deduced from the orthogonal constraints of two vanishing points. With the radial alignment constraint and the checkerboard corner point information, the initial values of the translation vectors (tx, ty) are first solved linearly, then that of tz is obtained after the establishment of a quadratic equation with one unknown, and finally, through minimizing the re-projection error of the checkerboard corner point, all the camera parameters except for the principal point are globally optimized and these optimized parameters are used for the correction of fisheye images. Two focus-fixed Hikvision fisheye cameras with different fields of view are selected for the calibration and image correction tests. The results show that the re-projection root mean square error (RMSE) of each camera for the proposed method is less than 1/3 pixel, and the calibration parameters can keep a good stability in the planar perspective correction effect at different areas of the fisheye image with the correction effect in the central region slightly better than that at the edge. The RMSE in the checkerboard corner point line fitting of the corrected fisheye images is less than 0.7 pixel which is obviously superior to that from the online calibration toolbox, and thus it has a relatively good application value.