We demonstrate an ink-jet printed ambipolar transistor and inverter based on a semiconducting carbon nanotube (CNT) network as a channel by employing a solution-based chemical doping technique with an amine-rich polyethyleneimine (PEI) polymer. The PEI polymer has been reported as an efficient electron dopant and thus contributes to enhancing n-type conduction in CNT transistors. However, because of the presence of ambient oxygen and moisture and the hygroscopicity of the PEI polymer, their p-type conduction did not seem to be effectively reduced, resulting in rather ambipolar conduction. Therefore, we utilize a simple solution-based doping technique to convert ptype semiconducting CNT transistors into ambipolar transistors and fabricate the ambipolar CNT transistor by combining a cost-effective ink-jet printing technique and a simple spin-coating method. Finally, the electrical performance of the logic inverter consisting of identical two ambipolar CNT transistors is also evaluated and optimized by adjusting the concentration of PEI polymer.