Novel push-pull polyenes containing non-aromatic cyclic olefines, such as cyclopentadiene, cyclopropene and cycloheptatriene, have been investigated for application of nonlinear optical (NLO) materials. Their dot products μβ0 of first hyperpolarizability (β0) and dipole moment (μ) are calculated by employing AM1/Finite Field and ZINDO/S approaches. Among them, the largest value is as high as 4.1×10-45 esu. The origin of such high μβ0 was analyzed based on the two-level model. Non-aromatic groups can transform to a stable aromatic anion/cation through gaining/losing an electron in their charge transfer states.