In this paper, we design a lightweight adaptive hybrid laminate metamaterial with higher design freedom for wave attenuation. The adaptive hybrid laminate acoustic metamaterials are composed of carbon-fiber-reinforced polymer (CFRP) and a periodic array of piezoelectric shunting patches attached to the laminate. A comprehensive analytical model is first developed to reveal the tunable wave attenuation capability in regard to the equivalent bending stiffness of lightweight adaptive hybrid laminate metamaterial. The tunable wave attenuation behavior has been confirmed through finite element modeling (FEM). Numerical results demonstrate that the lightweight adaptive hybrid laminate metamaterial with the shunting circuits can remarkably suppress wave propagation compared to the un-shunted case. In addition, the effects of the laminate’s parameters as well as the shunting circuits on the bandgap’s location and bandwidth are discussed. By introducing the negative capacitance shunting circuit into the piezoelectric patches, the bandwidth can be enlarged significantly.