Satellite monocular pose estimation usually extracts the keypoints of the satellite in the images, and then solves the PnP (perspective-n-points) problem to obtain the relative position and attitude between the camera and the satellite, in which the accuracy of satellite keypoints detection is the key to determine the accuracy of monocular pose estimation. To solve this problem, a high-precision satellite keypoints detection method was proposed, which predicted the image coordinates of the keypoints and gave the uncertainty of keypoints coordinate prediction synchronously. Then, a weighted PnP constraint equation was constructed to solve the relative position and attitude on this basis, which significantly improved the accuracy of satellite monocular pose estimation. Relevant experiments were carried out on the public satellite monocular pose estimation dataset named SPEED. The experimental results show that the proposed keypoints detection method for synchronously predicting keypoints coordinates and their uncertainty can significantly improve the accuracy of satellite keypoints detection,and by solving the weighted monocular pose estimation problem, the accuracy of satellite monocular pose estimation has been significantly improved.