The initial-value problem for hyperbolic equation d2u(t)/dt2+A(t)u(t)=f(t)(0tT), u(0)=ϕ,u(0)=ψ in a Hilbert space H with the self-adjoint positive definite operators A(t) is considered. The second order of accuracy difference scheme for the approximately solving this initial-value problem is presented. The stability estimates for the solution of this difference scheme are established.