A three-dimensional(3D) mathematical model of tumour growth at the avascular phase and vessel remodelling in host tissues is proposed with emphasis on the study of the interactions of tumour growth and hypoxic micro-environment in host tissues.The hybrid based model includes the continuum part,such as the distributions of oxygen and vascular endothelial growth factors(VEGFs),and the discrete part of tumour cells(TCs) and blood vessel networks.The simulation shows the dynamic process of avascular tumour growth from a few initial cells to an equilibrium state with varied vessel networks.After a phase of rapidly increasing numbers of the TCs,more and more host vessels collapse due to the stress caused by the growing tumour.In addition,the consumption of oxygen expands with the enlarged tumour region.The study also discusses the effects of certain factors on tumour growth,including the density and configuration of preexisting vessel networks and the blood oxygen content.The model enables us to examine the relationship between early tumour growth and hypoxic micro-environment in host tissues,which can be useful for further applications,such as tumour metastasis and the initialization of tumour angiogenesis. A three-dimensional (3D) mathematical model of tumor growth at the avascular phase and vessel remodeling in host tissues is proposed with emphasis on the study of the interactions of tumor growth and hypoxic micro-environment in host tissues. The hybrid based model includes the continuum part, such as the distributions of oxygen and vascular endothelial growth factors (VEGFs), and the discrete part of tumor cells (TCs) and blood vessel networks. The simulation shows the dynamic process of avascular tumor growth from a few initial cells to an equilibrium state with varied vessel networks. After a phase of rapidly increasing numbers of TCs, more and more host vessels collapse due to the stress caused by the growing tumor. addition, the consumption of oxygen expands with the enlarged region region. study also discusses the effects of certain factors on tumor growth, including the density and configuration of preexisting vessel networks and the blood oxygen content. model can u s to examine the relationship between early tumor growth and hypoxic micro-environment in host tissues, which can be useful for further applications, such as tumor metastasis and the initialization of tumor angiogenesis.