We report a fiber optic sensor for measuring the viscosity of Newtonian liquids. The sensing principle of the proposed sensor is based on sliding of liquid drop on an open air channel during which the liquid interacts with two decladded regions of an optical fiber. When liquid slides over the first decladded region, transmitted light intensity of the fiber undergoes an upward transition. As the liquid again slides over the second decladded region, another upward transition occurs. The time interval between the two transition events is known as transition time of the proposed sensor, and it is found to increase with increase in viscosity of the liquids when longitudinal displacement between the decladded regions and inclination of the flow channel are held constant.