A technique for determining the permeability of a phospholipid membrane on a single giant unilamellar vesicle (GUV) is described, which complements the existing methods utilizing either a planar black lipid membrane or sub-micrometre-sized liposomes. A single GUV is transferred using a micropipette from a solution of a nonpermeable solute into an iso-osmolar solution of a solute with a higher membrane permeability. Osmotical swelling of the vesicle is monitored with a CCD camera mounted on a phase contrast microscope, and a sequence of images is obtained. On each image, the points on the vesicle contour are determined using Sobel filtering with adaptive binarization threshold, and from these, the vesicle radius is calculated with great accuracy. From the time dependence of the vesicle radius, the membrane permeability is obtained. Using a test set of data, the method provided a consistent estimate of the POPC membrane permeability for glycerol, P = 1.7 x 10-8 m s-1, with individual samples ranging from 1.61 x 10-8 m s-1 to 1.98 x 10-8 m s-1. This value is -40% lower than the one obtained on similar systems. Possible causes for this discrepancy are discussed.