New double-layered electromagnetic absorbers are presented in this paper. The new absorbers composed of one lossy left-handed material absorbing layer and one impedance matching layer consisted of lossless right-handed material. It is indicated that the reflection loss of below -20dB can be obtained in the frequency range 7GHz-13GHz. Power attenuation achieving -50dB of narrow frequency band electromagnetic absorbers can also be obtained by modulate permittivity of right-handed material. Furthermore, the thickness of the whole absorbing structure is only 2mm, which is particularly helpful in some practical applications. The presented results are of reference significance for accurate design of the new electromagnetic absorbers and of practical prospects for stealth technology.