The EPR spectrum of an Eu^2+ impurity center in a SrMoO_4 single crystal in the temperature range T = 1.8, 111–300 K has been studied, and the temperature changes in the spin Hamiltonian parameters describing the EPR spectrum of odd europium isotopes have been determined. It is shown that small temperature changes in the diagonal parameters of the spin Hamiltonian (for odd Eu^2+ isotopes) ( T ) = b _2( F ) + b _2( L ) and ( T ) = P _2( F ) + P _2( L ) are explained by the compensation of spin–phonon contributions b _2( F ) and P _2( F ) by the contributions of the lattice thermal expansion b _2( L ) and P _2( L ). The quantities b _2( L ) and P _2( L ) that are dependent on the static lattice parameters at a given temperature, are estimated in terms of the superposition Newman model. Then, the spin–phonon b _2( F ) and P _2( F ) contributions determined by the lattice ion vibrations are separated. An analysis shows that ( F ) and ( F ) > 0, b _2( L ) and P _2( L ) < 0, and the temperature behavior of the spin–phonon contribution is well described by G. Pfister’s model of local vibrations.