We derive a model for describing the dynamics of imatinib-treated chronic myelogenous lekemia (CML). This model is a continuous extension of the agent-based CML model of Roeder et al. [Nature Medicine, 12(10), 1181-1184, 2006] and of its recent formulation as a system of difference equations [Kim, Lee, Levy, Bull. Math. Bio., 70, 2008 728-744]. The new model is formulated as a system of partial differential equations that describe various stages of differentiation and maturation of normal hematopoietic cells and of leukemic cells. An imatinib treatment is also incorporated into the model. The simulations of the new PDE model are shown to qualitatively agree with the results that were obtained with the discrete-time (difference equations and agent-based) models. At the same time, for a quantitative agreement, it is necessary to adjust the values of certain parameters, such as the rates of imatinib-induced inhibition and degradation.