In this work, the effective properties of heterogeneous centro-symmetric multi-laminated Cosserat composite materials with isotropic constituents are found by the two-scale asymptotic homogenization method (AHM). The local problems over the periodic cell derived by AHM are given and the analytical formulas of the effective properties are explicitly described. Numerical results for different periodic centro-symmetric laminated Cosserat composites are reported and discussed. The resulting composite belongs to the orthotropic symmetry under rotations of 90o about the unitary vector e3, that is, it is defined by eighteen effective independent properties: nine stiffness and nine torques.