Vacation policy describes the interruption of service process in engineering systems and management systems. Vacation queueing networks can be used to simulate these complex systems and have a wide range of applications in practice. Since the analytic formulas of the steady state distribution of vacation queueing networks are difficult to obtain, it is of great importance to study the numerical solution method. An algebraic multigrid algorithm is proposed for solving the steady state distribution of vacation queueing networks including two M/M/2 queues. With the special quasi-tridiagonal structure in the steady state equation, the prolongation and restriction operators of the multigrid algorithm are constructed by the cyclic reduction strategy. They are dependent on the coefficient matrix of linear system and therefore can maintain its characteristics on the coarser grid level, thus improving the convergence speed of the numerical algorithm. Finally, numerical examples show the superiority of the proposed algorithm.