In order to measure optical fiber connectors endface geometry parameters owith a high accuracy, a novel interferometer is proposed. In a Twyman-Green interferometcr, an optical shutter that opens or closes on command is placed between a beam splitter and a reference mirror. When the shutter is open, four interferograms are recorded in sequence with a CCD camera. Then the Carre phase-measurement technique and a new phase unwrapping algorithm are used to obtain the endface profile of the connector being measured. When the shutter is closed, what is captured by the CCD is the image of the fiber connector endface. Hough translation is used to accurately identify the fiber core center in the image. After the endface profile of the fiber connector and the location of the fiber core center are obtained, the endface geometry parameters are obtained by simple calculation. The measurement repeatability of the instrument, developed based on the above method, is as follows: radius(less than or equal to0.05%), apex offset (less than or equal to0.06mum), fiber height(less than or equal to5.5nm), and angle(less than or equal to0.0004degrees). Taking a test sample PC01 as an example, a comparison is made between results measured with the instrument and those measured with Dorc's ZX-1 mini PMS. The differences in radius, apex offset, fiber height and angle are 0.13 %, 3.96%, 4.35% and 3.85%, respectively. Hence the measurement accuracy of the instrument is comparable with that of the Dorc's ZX-1 mini PMS interferometer. The instrument has passed the test performed by the National Measurement and Test Center for East China.