Docking ring is a typical component on space vehicle, which can provide a single circle feature. But monocular vision pose estimation based on single circle with two solutions, which can not be applied to practical engineering application. In order to exclude the interference of false solution, a new method of removing the false solution using Euclidean distance invariance as a constraint is proposed to solve the pose ambiguity, and the paper gives the proof of a unique solution under the constraint. The error simulation analyses of the method are done, and feasible strategies to improve the measurement accuracy are given. According to the projection of the circle on the image, two pose solutions of the circle are calculated. Then a reference point on the circle supporting plane outside the circle is selected. The distance between the reference point and circle center is Euclidean invariant and prior knowledge, which can be used for a constraint to exclude the false solution to get the uniquely correct solution. The effectiveness and superiority of the method are verified by numerical simulation and experiments. Experimental results indicate that the method is robust to the noise, can get the right solution, requires least constraint conditions for the circle, and the calculation process is simple. Pose results are stable and reliable, and more accurate. The relative error of the circle center is less than 0.5%, and the absolute error of pose angle is less than 0.8°.