The stability of the negative ion of hydrogen (H^{-}) embedded in nonideal classical plasma has been studied by computing the ground state energy of the ion quite accurately. The interactions among the charged particles in plasma have been modelled by a pseudopotential, derived from a solution of Bogolyubov's hierarchy equations. An extensive basis set is employed in Rayleigh-Ritz variational method to compute the ground state energy of H^{-} for various values of plasma parameters. Effects of nonideality of plasma on the stability of the ion have been investigated in detail for a wide range of nonideality. Particular emphasis is made to compute accurately the critical values of the plasma screening parameters.