We theoretically investigate the ground state magnetic properties of the brownmillerite phase of SrCoO2.5. Strong correlations within Co d electrons are treated within the local spin density approximations of Density Functional theory (DFT) with Hubbard U corrections (LSDAU) and results are compared with the Heyd Scuzeria Ernzerhof (HSE) functional. The parameters computed with a U value of 7.5 eV are found to match closely to those computed within the HSE functional. A G type antiferromagnetic structure is found to be the most stable one, consistent with experimental observation. By mapping the total energies of different magnetic configurations onto a Heisenberg Hamiltonian we compute the magnetic exchange interaction parameters, J, between the nearest neighbor Co atoms. The J s obtained are then used to compute the spin wave frequencies and inelastic neutron scattering intensities. Among four spin wave branches, the lowest energy mode was found to have the largest scattering intensity at the magnetic zone center, while the other modes becomes dominant at different momenta. These predictions can be tested by experimentally.