Electronic and magnetic properties of the rare earth nitride EuN and Ga1-xEuxN (x = 0.0625) are studied with the full potential (linearized) augmented plane wave method plus local orbitals method. In this work we start our investigations by studying EuN using LDA and LDA+U. We will show the impact of LDA+U on the electronic properties. For Ga1-xEuxN we will present only the results related to the LDA+U method. It's found from the calculation of density of states (DOS) that the Eu-4f orbitals spin-polarize the host system and they are predominant in this diluted magnetic semi-conductor. The magnetic description is achieved by the calculation of spin densities difference contours and the magnetic moment.