The electronic structure of quasi-one-dimensional superconductor K2Cr3As3 is studied through systematic first-principles calculations. The ground state of K2Cr3As3 is paramagnetic. Close to the Fermi level, the , dxy, and orbitals dominate the electronic states, and three bands cross EF to form one 3D Fermi surface sheet and two quasi-1D sheets. The electronic DOS at EF is less than 1/3 of the experimental value, indicating a large electron renormalization factor around EF. Despite of the relatively small atomic numbers, the antisymmetric spin-orbit coupling splitting is sizable (≈60 meV) on the 3D Fermi surface sheet as well as on one of the quasi-1D sheets. Finally, the imaginary part of bare electron susceptibility shows large peaks at Γ, suggesting the presence of large ferromagnetic spin fluctuation in the compound.