The array-enhanced coherence resonance (AECR) in the diffusively coupled active rotators is investigated and its analysis with the nonlinear Fokker-Planck equation is presented. By considering the nonlinear Fokker-Planck equation of the rotators, it is found that the time-periodic solution exists in some parameter range. By solving the equation of a rotator and the Fokker-Planck equation simultaneously, the behavior of a rotator in the system with infinite number of rotators is considered, and it is found that AECR also takes place in this infinite system. Thus it is concluded that AECR is caused by the time-periodic solution of the probability density induced by noise.