An apparatus for measuring viscosity includes a container in which an inlet radius of an inlet end is larger than an outlet radius of an outlet end. A fluid with a flow velocity is placed in the container. The fluid has a density value and a pressure gradient value. A pressure controller for controlling the pressure gradient value of the fluid is connected to the inlet end and the outlet end. A flow meter measures the flow velocity. A viscosity of the fluid is correlated with the density value, the pressure gradient value, the inlet radius, the outlet radius and the flow velocity. After being applied to various fluids, the present invention improves testability. Moreover, the measurement time is reduced due to simple structure. The maintenance is easy and the operation is not complicated. Furthermore, less space is required, the cost is down and the measurement error is reduced.