The viscosity of biofluids can be used to acquire meaningful medical information on the conditions of a patient but has seldom been utilized in clinical practices owing to cumbersome measurement procedures and the need for large sample volumes. We present a colorimetric method to measure the viscosity of blood plasma using a paper-based viscometer developed in this study specifically for clinical diagnosis. The proposed analytical device consists of multilayered papers with fluid-loading, -mixing, and -measuring regions, and it can be fabricated readily in a simple manner using three-layered paper channels and tape. Moreover, the colorimetric analysis enables viscosity estimations by analyzing a single optical image. To validate the device performance, we measured the viscosities of fluids such as glycerin aqueous solutions, bovine-serum-albumin solution, dimethyl sulfoxide, and blood plasma. We found that the measured viscosities were in good agreement with the reference values. Finally, we developed a simple smartphone application for the viscosity measurements that helped enhance the convenience and utility of the paper-based viscometer while maintaining the measurement accuracy.