This paper proposes a privacy-preserving algorithm to solve the average-consensus problem based on Shamir's secret shar-ing scheme, in which a network of agents reach an agreement on their states without exposing their individual states until an agreement is reached. Unlike other methods, the proposed algorithm renders the network resistant to the collusion of any given number of neighbors (even with all neighbors' colluding). Another virtue of this work is that such a method can protect the network consensus procedure from eavesdropping.