This paper presents a distributed algorithm for the network size estimation problem. The problem is to find the total number of nodes in the network. The proposed algorithm utilizes the continuous-time dynamics for achieving synchronization, which provides a way to assign each element of the equilibrium point of the dynamics close to the network size. The algorithm guarantees that each node directly estimates the total number of nodes in the network. Moreover, the network size can be estimated regardless of initial condition. We also derive the stopping criteria of the algorithm and extend the result to the case where the network varies intermittently with time.