In this paper, a frequency selective absorber (FSA) with asymmetric performance is proposed. Modified log-periodic dipole array (LPDA) elements are applied to construct the FSA. With the ultra wide band (UWB) property of the LPDA-shaped elements, the FSA gets the UWB absorbing band. Due to the directionality of the LPDA, the FSA is asymmetric network which means that the reflection coefficients of the FSA are different when the incident wave lit the two surfaces respectively. Simulations and analysis are done to study the UWB and absorbing properties. The results show that the proposed FSA can effectively absorb or reflect the incident wave in 6.45GHz-20GHz when the incident wave lit the two surfaces respectively.