Fibre optic connectors are an important factor in the performance of fibre optical systems. In order to ensure good fibre-to-fibre contact, the endface geometry of fibre connectors needs to be measured quantitatively. In this paper, we present a vision-based automatic measurement system for the measurement of the endface geometry of a single-fibre connector. The optical set-up of the system developed is based on a Mirau objective interferometer, and a 3D profile of the connector endface is obtained by using phase-shifting techniques. Image-processing techniques are applied to automatically find the fibre centre and retrieve the geometric parameters of the connector endface, such as radius of curvature, apex offset and protrusion or undercut. Experimental results have demonstrated the feasibility of the proposed system.