The process by which the red blood cells are developed is known aserythropoiesis. It is depicted that while the process involves manycomponents, the ones are the erthrocytes themselves ant theerythropoietin hormone (EPO). The hemoglobin in the RBC absorbs theoxygen when it is flowing in the lung. The production and feedback loopin eryttropoiesis consist of RBC coming from the bone marrow. Amathematical model for this process which connecting the of erythrocytes(or RBC), the EPO and The oxygen is proposed together with time delay.A bifurcation analysis is carried out to determine the ranges of parametervalues that would lead to state productions of RBC. We have also shownthe computer simulations of the behaviors.Keywords: erythropoiesis, erythrocyte, bifurcation analysis, time delay