Current in vitro antitumor drug screening strategies insufficiently mimic biological systems. They tend to lack true perfusion and draining microcirculation systems, which may post significant limitations in explicitly reproducing the transport kinetics of cancer therapeutics. Herein, the fabrication of an improved tumor model consisting of a bioprinted hollow blood vessel and a lymphatic vessel pair, hosted in a 3D tumor microenvironment‐mimetic hydrogel matrix is reported, termed as the tumor‐on‐a‐chip with a bioprinted blood and a lymphatic vessel pair (TOC‐BBL). The bioprinted blood vessel is a perfusable channel with an opening on both ends, while the bioprinted lymphatic vessel is blinded on one end, both of which are embedded in a hydrogel tumor mass, with vessel permeability individually tunable through optimization of the compositions of the bioinks. It is demonstrated that systems with different combinations of these bioprinted blood/lymphatic vessels exhibit varying levels of diffusion profiles for biomolecules and anticancer drugs. The results suggest that this unique in vitro tumor model containing the bioprinted blood/lymphatic vessel pair may have the capacity of simulating the complex transport mechanisms of certain pharmaceutical compounds inside the tumor microenvironment, potentially providing improved accuracy in future cancer drug screening.