The aim of this paper is to introduce and analyze a new alternating direction implicit (ADI) Galerkin method for hyperbolic initial-boundary value problems. It has at least two advantages over the earlier similar methods: First, it involves only two time levels, so variable time steps can be used, and second, the initial conditions can be determined (imposed) in a very natural way. Optimal a priori \(H^ 1_ 0\)- and \(L^ 2\) error estimates are carried out in a standard way.