Based on the collinear and non-collinear magnetic structures, the ground state, magnetism and electronic structure of the frustrated triangular antiferromagnet AgCrO2 have been investigated using the density functional theory (DFT) within the generalized gradient approximation (GGA) with the projected augmented wave (PAW) method. Detailed magnetic structure has been elucidated vividly from the theoretical view. The calculations show that AgCrO2 magnetic ground state has 120° helical-spin order with its spiral plane parallel to the (110)or (11-0) plane. Due to the strong intra- and interlayer geometric spin frustration, parallel helical-spin chains arise along the a,b or a+b direction with the screw-rotation angle 120°. From the non-collinear electronic structure calculation, it is found that due to the spin frustration Cr-3d orbital states near the Fermi level become more localized, indicating an enhanced interaction between Cr-Cr. Nevertheless, the spin-orbit coupling has weak influence on the electron structure.