The outage performance fairness on asymmetric two-way amplify-andforward (AF) relaying networks is investigated. Power allocation is proposed to minimise maximum individual outage probability so as to maintain the balance between the two end nodes. It is shown that the outage performance fairness is finally achieved under various traffic requirements. Furthermore, the proposed power allocation can also obtain the system balance and improve the overall system outage performance compared with conventional uniform power allocation.Introduction: Recently there have been increasing research activities towards two-way relaying [1], which has been recognised as a promising approach to mitigate the spectral efficiency loss of conventional one-way relaying systems [2]. Of particular interest is two-way amplify-andforward (AF) relaying networks [3,4]. Specifically, for a more efficient use of the power resources, considerable attention has been concentrated on the power allocation [5,6]. In [5], the power allocation is employed to achieve the trade-off of outage probability between two terminals under a total power constraint. In [6], optimal power allocation is carried out to obtain data rate fairness on the two-way relay channel. However, most of the research contexts of the above works are limited to the idealistic assumption that the system operates in the symmetric traffic mode. In asymmetric traffic mode, one direction transmission may face outage with the other direction transmission at a certain data rate, even though data rate fairness [6] is achieved. Therefore, to ensure that both nodes play an identical role in the transmission, it makes more sense to study the outage performance fairness for asymmetric twoway AF relaying networks.In this Letter, we extend the existing work in [6], and consider outage performance fairness on asymmetric two-way AF relaying networks. We address the problem of power allocation for improving the poorer one's outage performance under a total power constraint so as to obtain an outage balance between the two end nodes. Unlike [6], only statistical information of the channel is needed in the proposed power allocation rather than the instantaneous channel information, thus lowering the implementation complexity.Notations: We use x CN (a, b) to denote a complex Gaussian random variable x with mean a and variance b. Pr[·] and | · | denote probability and absolute value, respectively.