The electronic structure and magnetic exchange interactions of the ladder vanadate CaV2O5 have been studied by ab initio electronic structure calculations based on density functional theory (DFT). Geometry optimization and electronic structure calculations are performed using spin-polarized generalized gradient approximation (GGA) exchange-correlation functionals for four possible spin-ordered states. The experimentally observed insulating behavior has been reproduced successfully in the framework of the band theory by considering the magnetic ordering. Calculated results reveal that the true magnetic ground state of CaV2O5 is the antiferromagnetic (AFM) state with AFM exchange interactions both inside the rungs and along the ladder legs. Calculated exchange parameters indicate that the ladder structural vanadate CaV2O5 should be described as weakly coupled dimer system rather than as spin ladder compound. The AFM interactions inside the dimer are crucial to the insulating ground state and magnetic characteristics of CaV2O5.