This paper is devoted to measuring the security of cyber networks under advanced persistent threats (APTs). First, an APT-based cyber attack-defense process is modeled as an individual-level dynamical system. Second, the dynamic model is shown to exhibit the global stability. On this basis, a new security metric of cyber networks, which is known as the limit security, is defined as the limit expected fraction of compromised nodes in the networks. Next, the influence of different factors on the limit security is illuminated through theoretical analysis and computer simulation. This work helps understand the security of cyber networks under APTs.