Detailed X-band (about 9.5 GHz) electron paramagnetic resonance (EPR) measurements were carried out at 295, 77 and 4.2 K on the Eu2+ ion in a Pb1-xEuxSe single crystal. The values of the spin-Hamiltonian parameters have been determined by a simultaneous fitting of all the EPR line positions recorded for various orientations of the external magnetic field in the [010] plane using a rigorous least-squares fitting procedure. The absolute sign of the zero-field splitting parameter b4 was determined to be positive from the relative intensities of lines at liquid-helium temperature (4.2 K). The excellent fit of the line positions to a cubic spin Hamiltonian confirms that the site symmetry for Eu2+ ions is, indeed, cubic in the Pb1-x,Eux,Se single crystal over the temperature range 4.2-295 K. The Dynosian shape of the EPR lines indicates the metallic nature of the Pb1-xEuxSe sample. The nearest-neighbour Eu2+-Eu2+ exchange interaction has been estimated to be 20.4 GHz (antiferromagnetic) from the exchange pair EPR spectrum at 4.2 K. The hyperfine interaction constants for the isotopes 151Eu and 153Eu have been estimated.