Advanced persistent threats (APTs) pose a grave threat to cyberspace, because they deactivate all the conventional cyber defense mechanisms. This paper addresses the issue of evaluating the security of the cyber networks under APTs. For this purpose, a dynamic model capturing the APT-based cyber-attack-defense processes is proposed. Theoretical analysis shows that this model admits a globally stable equilibrium. On this basis, a new security metric known as the equilibrium security is suggested. The impact of several factors on the equilibrium security is revealed through theoretical analysis or computer simulation. These findings contribute to the development of feasible security solutions against APTs.