Currently, the manufacturing process of the calibration equipment suitable for near-infrared cameras is complex and expensive. This increases the development cost of the optical surgical navigation system. Simultaneously, owing to the lack of reliable feature point centers extraction method, it is difficult to have an error-free positioning accuracy of the navigation system. To address this, we use LEDs to design a target suitable for near-infrared cameras, inspired by the hardware structure of circular marker array target. A sorting method with unique result is proposed, and the ellipse fitting method is improved. During feature point extraction, we used Otsu thresholding for preprocessing. Subsequently, we applied a Gaussian kernel convolution based on the average radius of the feature points to attenuate the scattering halo of the LEDs and then used Zernike moment to detect the subpixel edges of the feature points and remove some abnormal edges. Furthermore, we performed secondary fitting to obtain more accurate center coordinates of feature points. Finally, we completed the stereo near-infrared camera calibration using Zhang's method. Experimental results show that, after removing some abnormal edges, the reprojection error is reduced by approximately 3% and standard deviation of the stereo reconstruction samples is reduced by approximately 3.3%.