Summary: An unconditionally stable alternating direction implicit (ADI) method of \(O(k^2+ h^2)\) of M. Lees type [J. Soc. Ind. Appl. Math. 10, 610-616 (1962; Zbl 0111.29204)] for solving the three space dimensional linear hyperbolic equation \(u_{tt}+ 2\alpha u_t+ \beta^2u= u_{xx}+ u_{yy}+ u_{zz}+ f(x,y,z,t)\), \(0< x, y\), \(z< 1\), \(t> 0\) subject to appropriate initial and Dirichlet boundary conditions is proposed, where \(\alpha> 0\) and \(\beta\geq 0\) are real numbers. For this method, we use a single computational cell. The resulting system of algebraic equations is solved by a three step split method. The new method is demonstrated by a suitable numerical example.