Blood viscosity is influenced by several factors, including red blood cell (RBC) deformability, hematocrit (Hct), and plasma protein levels. To effectively isolate the individual contributions of several factors, it is necessary to simultaneously measure the viscosities of the blood and plasma. In this study, the viscosities of suspended blood and plasma were obtained sequentially by adopting an ultrasonic transducer for plasma separation and a co-flowing microfluidic channel for viscosity measurement. To improve the measurement accuracy of viscosity, the correction factor was obtained through experiments and numerical simulations, which was then inserted into the analytical expression for viscosity. To stabilize the pulsatile blood flow resulting from a micropump, the frequency (f) and voltage (v) were set to f = 300 Hz and v = 140 au, respectively. Flexible polyethylene tubing (i.d. = 500 µm, length = 40 mm) was connected to the microfluidic device as an air damper. Consequently, the coefficient of variance of the blood velocity decreased by up to 1%. As a demonstration, suspended blood (Hct = 20%, 30%, and 40%) was prepared by adding normal RBCs to autologous plasma. Compared with the previous method, the present method overestimates the viscosity values of both the fluids (i.e., suspended blood: 14–25% and plasma: 7–21%). The present method has the ability to sequentially measure the viscosities of suspended blood and plasma. The integrated system contributes to reducing blood-handling procedures (i.e., blood collection, blood loading into the syringe, and syringe installation into the syringe pump).