In this research, structural, electronic, and magnetic properties of Strontium mono ferrite ceramic were studied. The calculations were performed by Full-Potential-Linearized Augmented Plane Wave method in the framework density functional theory with different approximations. The results suggest that among the four states of nonmagnetic, ferromagnetic, antiferromagnetic, and ferrimagnetic of SrFe2O4, ferrimagnetic is the most stable state. Generalized Gradient and Local Spin Density approximations were not an appropriate approach to calculate the band gap and magnetic moment of the compound. Therefore, other approximations such as GGA+U, LSDA+U, and modified Becke-Johnson were used. Band gap and lattice constants improved using these approximations. The Hubbard parameter was calculated (U-eff=4.5eV) by an ab initio method. Then, the electronic properties of SrFe2O4 such as band gap, exchange constant, and magneto crystalline anisotropy as well as the influence of pressure on these properties were investigated by using GGA+U approximation. Calculated magnetic moment for strontium mono ferrite is equal to 2.72(B) in the semiconductor state. Lattice constant results are in consistent with experimental studies. However, the amounts for bulk modulus, magnetic moment, and band gap have been not estimated experimentally.