Blood flows in microcirculation are determined by the mechanical properties of blood samples, which have been used to screen the status or progress of diseases. To achieve this, it is necessary to measure the viscoelasticity of blood samples under a pulsatile blood condition. In this study, viscoelasticity measurement is demonstrated by quantifying interface variations in coflowing streams. To demonstrate the present method, a T-shaped microfluidic device is designed to have two inlets (a, b), one outlet (a), two guiding channels (blood sample channel, reference fluid channel), and one coflowing channel. Two syringe pumps are employed to infuse a blood sample at a sinusoidal flow rate. The reference fluid is supplied at a constant flow rate. Using a discrete fluidic circuit model, a first-order linear differential equation for the interface is derived by including two approximate factors (F1 = 1.094, F2 = 1.1087). The viscosity and compliance are derived analytically as viscoelasticity. The experimental results showed that compliance is influenced substantially by the period. The hematocrit and diluent contributed to the varying viscosity and compliance. The viscoelasticity varied substantially for red blood cells fixed with higher concentrations of glutaraldehyde solution. The experimental results showed that the present method has the ability to monitor the viscoelasticity of blood samples under a sinusoidal flow-rate pattern.