The nonlinear parametric interaction of the MHD Alfven wave (pumping wave) with kinetic Alfven wave in the space plasma with small plasma parameter β is investigated on the basis of two-fluid magnetohydrodynamics. A nonlinear dispersion relation describing the three-wave interaction, instability growth rate and the time of instability development are found. The nonlinear parametric processes studied here can take place in the plasma of the solar corona and in the Earth magnetosphere.