Secure and fair transmission is essential for wireless-powered backscatter communication networks (WPBCNs), which has not been taken seriously enough by the existing works. In this letter, we consider a multi-tag WPBCN in the presence of an eavesdropper, where a power station (PS) serves multiple tags which backscatter wireless information to a reader. Furthermore, the artificial noise (AN) is transmitted from the PS to impair the eavesdropping capability for security deliberately. An energy efficiency (EE)-based resource allocation problem with max-min fairness is formulated by jointly optimizing the backscattering time, the power ratio of the AN, and the reflection coefficient of each tag, where imperfect channel state information and non-linear energy harvesting models are considered. To tackle its non-convexity, we propose a Dinkelbach-based iterative algorithm to obtain the sub-optimal solution. Simulation results verify the effectiveness of the proposed algorithm.