This work studies secure communications for a cell-free massive multiple-input multiple-output (CF-mMIMO) network which is attacked by multiple passive eavesdroppers overhearing communications between access points (APs) and users in the network. It will be revealed that the distributed APs in CF-mMIMO allows not only legitimate users but also eavesdroppers to reap the diversity gain, which seriously degrades secrecy performance. Motivated by this, this work proposes an artificial noise (AN)-aided secure power control scheme for CF-mMIMO under passive eavesdropping aiming to achieve a higher secrecy rate and/or guarantee security. In particular, it will be demonstrated that a careful use of AN signal in the power control is especially important to improve the secrecy performance. The performance of the proposed power control scheme is evaluated and compared with various power control schemes via numerical experiments, which clearly shows that the proposed power control scheme outperforms all the competing schemes.