Red blood cell (RBC) aggregation and erythrocyte sedimentation rate (ESR) are considered to be promising biomarkers for effectively monitoring blood rheology at extremely low shear rates. In this study, a microfluidic-based measurement technique is suggested to evaluate RBC aggregation under hematocrit variations due to the continuous ESR. After the pipette tip is tightly fitted into an inlet port, a disposable suction pump is connected to the outlet port through a polyethylene tube. After dropping blood (approximately 0.2 mL) into the pipette tip, the blood flow can be started and stopped by periodically operating a pinch valve. To evaluate variations in RBC aggregation due to the continuous ESR, an EAI (Erythrocyte-sedimentation-rate Aggregation Index) is newly suggested, which uses temporal variations of image intensity. To demonstrate the proposed method, the dynamic characterization of the disposable suction pump is first quantitatively measured by varying the hematocrit levels and cavity volume of the suction pump. Next, variations in RBC aggregation and ESR are quantified by varying the hematocrit levels. The conventional aggregation index (AI) is maintained constant, unrelated to the hematocrit values. However, the EAI significantly decreased with respect to the hematocrit values. Thus, the EAI is more effective than the AI for monitoring variations in RBC aggregation due to the ESR. Lastly, the proposed method is employed to detect aggregated blood and thermally-induced blood. The EAI gradually increased as the concentration of a dextran solution increased. In addition, the EAI significantly decreased for thermally-induced blood. From this experimental demonstration, the proposed method is able to effectively measure variations in RBC aggregation due to continuous hematocrit variations, especially by quantifying the EAI.