Structure from motion (SfM) has been treated as a mature technique to carry out the task of image orientation and 3D reconstruction. However, it is an ongoing challenge to obtain correct reconstruction results from image sets consisting of problematic match pairs. This paper investigated two types of problematic match pairs, stemming from repetitive structures and very short baselines. We built a weighted view-graph based on all potential match pairs and propose a progressive SfM method (PRMP-PSfM) that iteratively prioritizes and refines its match pairs (or edges). The method has two main steps: initialization and expansion. Initialization is developed for reliable seed reconstruction. Specifically, we prioritize a subset of match pairs by the union of multiple independent minimum spanning trees and refine them by the idea of cycle consistency inference (CCI), which aims to infer incorrect edges by analyzing the geometric consistency over cycles of the view-graph. The seed reconstruction is progressively expanded by iteratively adding new minimum spanning trees and refining the corresponding match pairs, and the expansion terminates when a certain completeness of the block is achieved. Results from evaluations on several public datasets demonstrate that PRMP-PSfM can successfully accomplish the image orientation task for datasets with repetitive structures and very short baselines and can obtain better or similar accuracy of reconstruction results compared to several state-of-the-art incremental and hierarchical SfM methods.