Monolayer (ML) graphdiyne, a two-dimensional semiconductor with appropriate band gap and high carrier mobility, is a promising candidate for channel material in field effect transistors (FETs). Using density functional theory combined with non-equilibrium Green's function method, we systematically investigate the contact and transport properties of graphdiyne FETs with various electrodes, including metals (Cu, Au, Ni, Al and Ag) and MXenes (Cr2C, Ta2C and V2C). Strong interaction can be found between ML graphdiyne and the Cu, Ni and MXenes electrodes with indistinguishable band structure of ML graphdiyne, while weak or medium interaction exists in the contacts of ML graphdiyne and the Au, Al and Ag electrodes where the band structure of ML graphdiyne remains intact. Despite the different contact interactions, Ohmic contacts are generated with all considered electrode materials owing to the weak Fermi level pinning of graphdiyne. The linear I-V characteristic curve verifies the Ohmic contact between Au electrode and graphdiyne ultimately. The theoretically calculated Schottky barrier heights of graphdiyne with Cu electrode are consistent with the available experimental data. Our calculation suggests that graphdiyne is an excellent channel material of FETs forming desired Ohmic contacts with wide-ranging electrodes and thus is promising to fabricate high performance FETs.