In order to study well-posed problem of the numerical solutions method for Zakharov equations in plasma physics, first, according to the periodic initial value problem of the equations, a semi-discrete Fourier spectral scheme is constructed in the closed region of [0, T]. Second, the conservative property of the semi-discrete spectral scheme is proved. And at last, the conservative property is used to obtain the priori estimate of approximate solution and the existence of global solution for Zakharov equations.