We theoretically study wave properties for one-dimensional defective asymmetric photonic crystals, air/(AB)MG(BA)N/air, air/(AQ)MG(QA)N/air, and air/(BQ)MG(QB)N/air, where A is a lossy epsilon-negative material, B is a lossy mu-negative material, G and Q are dielectrics with different refractive indexes, and M and N are stack numbers with M≠N. Special attention has been paid to their absorption spectra. It is found that at certain frequencies the absorption can exhibit unidirectional properties. Our calculated results show two kinds of unidirectional absorption peaks. One is a single absorption peak whose frequency depends on the thickness of defect layer G. For the other peaks, its frequency does not change when the defect layer's thickness changes. In addition, in the second kind of peaks, the peak numbers for forward and backward propagation are different, that is, there are (M-1) absorption peaks for forward propagation, while there are (N-1) absorption peaks for backward propagation. When the two kinds of unidirectional absorption peaks are merged, some new peaks appear, and both forward and backward propagation will have (M+N-1) absorption peaks.