The blood flow in horizontal veins is studied before without consideration of gravity term and constant pressure gradient. This study examines the effects of suction and gravity on the blood flow in the peristaltic horizontal vein of Henle (GCT, gastro-colic venous trunk). The blood flow in the peristaltic horizontal vein of Henle (GCT) is considered as an incompressible and viscous Newtonian fluid properties. Equations for Navier-Stokes, concentration, volume rate, and mass conservation define the mathematical model of the current problem. When blood has long blood wavelengths and a low Reynolds number, the analytical solutions are obtained under the influence of the amplitude ratio, blood diffusion coefficient, Grashof number, and suction process parameter. The pressure gradient, the blood velocity, the blood concentration, and the stream function of the blood flow are obtained. The blood concentration proportional inversely with suction process. On contrary the blood velocity increases under the effect of suction process. The results are shown in several graphs for different values of the physical parameters. The majority of diseases need to the suction process as a wet and dry cupping therapy treatments to avoid the blood clots appeared.