The interface between mathematics and biology has initiated and fostered new mathematical areas, where the ideas from mathematics and biology are synergistically applied. Study of fluid dynamics plays a significant role in fluid flow inside the human body, and modeling of blood flow is an important field in cardiovascular physics. However, models have been developed so far are very complex with three-dimensional analysis. This paper presents a novel and simple mathematical model of the blood flow and the blood pressure. The main fluid component of the cardiovascular system is the blood which flows through the different blood vessels in the body. Although blood is the non-Newtonian fluid, in many cases, it behaves like a Newtonian fluid which is governed by the Navier-Stokes equations. With the help of continuity equation and the Navier-Stokes equations, a simple differential equation was derived under some assumption, which is called as the cardiovascular system equation. Then by applying the logical assumptions on this Cardiovascular System equation, the general mathematical model of the normal blood flow was developed. Then this model was extended for normal blood pressure using the Poisuelli's equation. At the end of this study, some analysis had been performed to determine the validity of the proposed model. The analysis showed that the model can satisfy both the different properties of blood flow and blood pressure.