Red blood cells play an extremely important role in human metabolism, and the study of hematopoietic models is of great significance in biology and medicine. A kind of semi-discrete hetmatopoietic model named Mackey-Glass Model was proposed and analyzed in this paper. The existences, stabilities, and local dynamics of the fixed points were discussed. By using bifurcation theory, we studied the Neimark-Sacker bifurcation, saddle-node bifurcation, and strong resonance of 1:4. The numerical simulations were presented to illustrate the results of theoretical analysis obtained in this paper, and complex dynamical behaviors were found such as invariant cycles, heteroclinic cycles and Li-Yorke chaos. In addition, a new periodic bubbling phenomenon was discovered in numerical simulations. These not only reflect the richer dynamical behaviors of the semi-discrete models, but also some reflect the complex metabolic characteristics of the hematopoietic system under environmental intervention.