In this paper, the change of pressure in the circulation of blood and viscous blood concentration in a vertical Colic vein are studied. The mass, concentration, and Navier-Stokes equations introduce the mathematical simulation in case of long wavelength and low Reynolds number. The analytical results introduced that the gradient pressure affected with modified Grashof number, vein radius and inversely with blood viscosity. Moreover, the blood concentration, and velocity of blood is very sensitive for the small change of blood density ratio, amplitude ratio and vein length. we focus the study for the change of pressure in the circulation of blood in a vertical colic vein, the concentration and velocity of blood. The peristaltic velocity of blood flow is obtained as a function of some physical parameters. The analytical solutions are obtained for concentration distribution of blood, blood velocity and change of pressure under the effect of modified Grashof number, initial concentration and blood viscosity.