Pose estimation of a three-dimensional (3D) rigid object based on monocular vision is a fundamental problem in computer vision. Existing methods usually presume that there is a certain feature projection correspondence available a priori between the input image and object's 3D model, which substantially reduces the mathematical complexity of the problem. However, in actual applications this presumption rarely holds. How to estimate the pose of a general 3D object with no feature projection correspondence available a priori is still not well resolved. In this study, the authors propose a new 3D rigid object pose estimation method based on object's contour and non-Euclidean multi-feature distance map, which solves both the pose estimation problem and the feature projection correspondence problem simultaneously and iteratively. Experiment results show that our method also has good performance in convergence speed, convergence radius and noise robustness.