A magnetic microroller, inspired by leukocytes (also called white blood cells, WBCs) in the microcirculatory system, represents a promising candidate for targeted drug delivery. However, the rolling dynamics of an individual microroller in response to controlled changes in shear stress and magnetic fields remains largely unknown. Here, we develop a mesoscopic model of the WBC-inspired microroller to investigate its locomotion behavior inside blood vessels under different shear stresses and magnetic torques. We find that the microroller can roll along with the blood flow or move against the bloodstream depending upon the competition between the applied magnetic torque and fluid shear stress. Our simulations reveal that the microroller can achieve precise navigation under low shear stress levels. We also probe the effect of the blood hematocrit on the dynamic performance of the microroller, which shows that shear-induced collisions between erythrocytes (also called red blood cells) and the microroller can significantly alter the motion of the microroller, especially under high hematocrit levels. In addition, we examine the rolling dynamics of the WBC-inspired microroller in a bifurcating microfluidic channel, demonstrating that the microroller can navigate along the user-defined path. These findings provide unique insights into the rolling dynamics of the individual microroller in physiologically relevant blood flow and offer an objective way for facilitating the design of bioinspired microrollers in targeted and localized therapeutic delivery with high precision and efficiency.