Diagnosis of plus disease is crucial for timely treatment and management of retinopathy of prematurity. An indicator of the presence of plus disease is an increase in the tortuosity of blood vessels in the retina. In this work, we propose a new angle-variation-based measure for quantification of tortuosity in retinal fundus images of preterm infants. The methods include the use of Gabor filters to detect vessels as well as to obtain their orientation at each pixel. Morphological image processing methods are used to obtain a skeleton image of the vessels for measurement of tortuosity. Out of 11 vessel segments, marked by an expert ophthalmologist as showing high levels of tortuosity due to plus disease, all were correctly identified using the proposed methods.