There are so many non-Newtonian fluids in our daily life, such as milk, blood, cytoplasm, and mucus, most of which are viscoelastic heterogeneous liquid containing cells, inorganic ion, metabolites, and hormones. In microfluidic microparticle-manipulating applications, the target particles are practically distributed within the biological fluids like blood and urine. The viscoelasticity of biological fluid is constantly ignored for simplicity especially when the fluid is substantially diluted and contains rather complex components. However, even the fluid’s ultraweak viscoelasticity actually affects the microparticle migration and may bring a completely different behavior compared with the Newtonian fluids. As a result, a robust and easy operated on-chip viscoelasticity sensor is potential and desired in many research and industrial fields, including assay sample preparation, clinical diagnostics, and on-chip sensor. In this work, we employed stable non-Newtonian fluid–polyethylene oxide (PEO) solutions with various concentrations to investigate and calibrate effects of the weak fluidic viscoelasticity on microparticle behaviors in a double-layered microfluidic channel. An analogy-based database of fluidic patterns for viscoelasticity sensing and relaxation time measurement was established. Then, we tested different biological fluids including blood plasma and fetal bovine serum and proved that they exhibited similar viscoelasticity effects to the PEO solutions with the corresponding concentration, which reached a good agreement with available results by references. The detection limitation of relaxation time can reach 1 ms. It promised a robust and integrated on-chip microfluidic viscoelasticity sensor for different biological fluids without complicated calculations.