In this paper, a piezoelectric biomedical nanosensor (PBMNS) based on cylindrical nanoshell subjected to nonlinear electrostatic field and viscoelastic medium is introduced to investigate natural frequency and stability analysis of PBMNS conveying viscous bloodstream using the electro-elastic Gurtin--Murdoch surface/interface theory, Hamilton's principle and assumed mode method combined with Euler -- Lagrange. The effect of different parameters on natural frequencies and stability analysis of PBMNS is demonstrated. It is shown that bloodstream velocity due to motion of biomarkers has major unpredictable effects on natural frequency and critical fluid velocity of the system and one should precisely consider their effects.