A hybrid discrete-continuum model of tumor growth in the avascular phase considering capillary points is established. The influence of the position of capillary points on tumor growth is also studied by simulation. The results of the dynamic tumor growth and the distribution of oxygen, matrix-degrading enzymes, and extracellular matrixconcentration in the microenvironment with respect to time are shown by graphs. The relationships between different oxygenated environments and the numbers of surviving, dead, proliferative, and quiescent tumor cells are also investigated.