The recent discovery of cancer stem cells (CSCs), or tumor initiating cells (TICs), in a variety of cancers, including breast cancer, provides a key to understand the processes of tumor initiation, progression and recurrence. Here, we present a three-dimensional (3D) multiscale model of the CSC-initiated tumor growth, which takes into account essential microenvironmental (mE) factors (e.g. nutrients, extracellular matrix) and some important biological traits (e.g. angiogenesis, cell apoptosis, and necrosis) and addresses tumor growth from three different levels, i.e. molecular, cellular and tissue levels. At the molecular level, mathematical diffusion-reaction equations are used to understand the dynamics of mE factors. At the cellular level, a cellular automaton is designed to simulate the life cycle and behaviors of individual cells. At the tissue level, a computer graphics method is used to illustrate the geometry of the whole tumor. The simulation study based on the proposed model indicates that the content of CSCs in a tumor mass plays an essential role in driving tumor growth. The simulation also highlights the significance of developing therapeutic agents that can deliver drug molecules into the interior of the tumor, where most of CSCs tend to reside. The simulation study on the breast cancer xenografts reveals that the mouse tumor initiated from a mixed population of human CSCs and other tumor cells show a faster growth rate, while a weaker proliferation and aggressiveness than that initiated from a pure human CSCs population. These simulation results are mostly consistent with our experimental observations. The mathematical model thus provides a new framework for the modeling and simulation studies of CSC-initiated cancer development.