Formation of Ohmic contact is crucial for achieving high device performance in two-dimensional (2D) materials based transistors. By using ab initio electronic structure calculations and quantum transport simulations, we reveal the great potential of 2D titanium carbides as the electrode materials for monolayer (ML) WSe2 device. In the vertical direction, both tunnel barrier and Schottky barrier are absent in all the three hybrid heterostructures of ML WSe2/Ti2C and ML WSe2/Ti2CY2 (Y = F and OH), implying a high vertical carrier injection efficiency. In the lateral direction, although pristine Ti2C and ML WSe2 form a Schottky contact with electron barrier of 0.40 eV, Ti2CF2/ML WSe2 and Ti2C(OH)2/ML WSe2 form p-type quasi-Ohmic and n-type Ohmic contacts, respectively. Therefore, 2D titanium carbides can be promising candidates as electrode materials for the ML WSe2 transistors by proper controlling of the surface functional group.