Monolayer (ML) Tl2O, as a newly discovered metal-shrouded two-dimensional semiconductor with an appropriate bandgap and high carrier mobility, is a promising candidate as the channel materials for the next-generation field-effect transistors (FETs). Using ab initio electronic structure calculation and quantum transport simulation, the contact properties of ML Tl2O-metal interfaces based on FET are comprehensively investigated with Au, Sc, Tl, Ni, graphene, Ti2C, Ti2CF2, and Ti2C(OH)(2) electrodes. ML Tl2O undergoes metallization with Au, Sc, Tl, Ni, and Ti2C, while it forms van der Waals-type contact with graphene, Ti2CF2, and Ti2C(OH)(2). An n-type lateral Schottky contact is formed with Ni, Au, Sc, and Ti2C electrodes with the electron Schottky barrier height (SBH) of 0.25, 0.27, 0.27, and 0.36 eV, respectively, while a p-type lateral Schottky contact is formed with graphene electrode with the hole SBH of 0.10 eV. Surprisingly, a desired n-type Ohmic contact arises with Tl and Ti2C(OH)(2) electrodes and a desired p-type Ohmic contact arises with Ti2CF2 electrode. The study not only provides a deep understanding of the interfacial properties of the ML Tl2O FETs but also reveals a versatile approach to realize both n- and p-type Ohmic contact for the ML Tl2O FETs.