Aligned carbon-nanotube (CNT) sheets are used as building blocks to prepare light-weight, frequency-tunable and high-performance microwave absorbers, and the absorption frequency can be accurately controlled by stacking them with different intersectional angles. A remarkable reflection loss of -47.66 dB is achieved by stacking four aligned CNT sheets with an intersectional angle of 90° between two neighboring ones. The incorporation of a second phase such as a metal and a conducting polymer greatly enhances the microwave-absorption capability.