In this paper, a model of neutrophils and monocytes production from uniform colony-forming unit of granulocytic- macrophage series in red bone marrow is proposed. The model considers the presence of cells in a G0 stage, mitosis, and cell transition speed between stages of maturation. The mitosis is described with a logistic equation. Transition speeds and cell growth are calculated for the conditions of normal hematopoiesis, and the white blood count at every stage is estimated. A graphical presentation of cell population growth at every stage of cell maturing is provided. It is shown that cell count growth tends to be exponential at the beginning and stable at the moment of homeostasis. The proposed model operates with a large number of parameters in equations describing each fraction of maturing cells. This allows the model to consider the influence of various factors on specific elements of leukopoiesis system without the limitation to the whole system only. Additionally, a large number of model parameters for each stage provides a possibility for more exact and detailed description of leukopoiesis stages that is prospective for usage in clinical practice.