We investigate a problem for a model of a non-Newtonian micropolar fluid coupled system. The problem has been considered in a bounded, smooth domain ofR3with Dirichlet boundary conditions. The operator stress tensor is given byτ(e(u))=[(ν+ν0M(|e(u)|2))e(u)]. To prove the existence of weak solutions we use the method of Faedo-Galerkin and compactness arguments. Uniqueness and periodicity of solutions are also considered.