Viscosity measurements have a wide range of applications from industrial chemical production to medical diagnosis. In this work, we have developed a simple droplet-based, water-in-oil continuous viscometer capable of measuring viscosity changes in 10 s or less and consuming a total sample volume of less than 1 μL/h. The viscometer employs a flow-focusing geometry and generates droplets under constant pressure. The length of the droplets (Ld) is highly correlated to the aqueous-phase viscosity (μaq) at high ratios of aqueous-inlet to oil-inlet pressure (AIP/OIP), yielding a linear relationship between μaq and 1/(Ld - Lc) where Lc is the minimal obtainable droplet length and approximately equals to the width of the droplet-generating channel. Theoretical analysis verifies this linear relationship, and the resulting equations can be used to optimize the design of the device such as the channel width, depth, and length. The viscometer can be used for Newtonian fluids and, by accurately calculating the shear rate, for non-Newtonian fluids such as Boger fluids and shear thinning fluids. In these latter cases, the shear rates depend on the velocity of the aqueous phase and can be adjusted by varying the input pressures. The applicable range of viscosity measurements depends on the oil-phase viscosity (μoil), and viscosities within the range of 0.01-10 μoil can be measured reliably with less than 5% error.