A tumor in a normal tissue will introduce some significant physiological and pathological changes to the adjacent normal tissues. To quantitatively study how the tumor affects the partial oxygen pressure (PO2) distribution in a normal tissue, an improved Krogh’s cylinder model that is more realistic than an assumption of homogeneous PO2 distribution in a certain region is used to describe the oxygen diffusion from a capillary into its surrounding tissue. In this study, a comparison of the oxygen transport in a normal tissue without tumors and with an implanted tumor is presented. The results show that when a tumor is implanted at the upstream part of a capillary, the entire surrounding normal tissue that is located at the downstream part of the capillary suffers from a low level of oxygen, and the PO2 in the normal tissue decreases by an average of 16%. In contrast, a tumor located at the downstream part of a capillary makes a slight impact on the PO2 distribution in the upstream normal tissue. However, in both situations, a part of the tumor mass that is far from the capillary is in the quiescent even necrotic status due to the lack of sufficient supply of oxygen.