Wormhole solutions are discussed for two different physical situations in the background of a homogeneous anisotropic space-time. In the first case, the wormholes are solutions of the Euclidean Einstein equations with a cosmological constant and a two-index antisymmetric tensor for monopole configuration on a space with three-surface of topology S1 X S2. In the second step, conformal scalar field is coupled to gravity and wormhole are considered for both lambda = 0 and lambda > 0. These results are analogous to the wormhole solutions for FRW metric.