In this letter, we first propose a Zeroth-Order cOordinate Method (ZOOM) to solve the stochastic optimization problem over a decentralized network with only zeroth-order (ZO) oracle feedback available. Moreover, we equip a simple mechanism “powerball” to ZOOM and propose ZOOM-PB to accelerate the convergence of ZOOM. Compared with the existing methods, we verify the proposed algorithms through two benchmark examples in the literature, namely the black-box binary classification and the generating adversarial examples from black-box DNNs in order to compare with the existing state-of-the-art centralized and distributed ZO algorithms. The numerical results demonstrate a faster convergence rate of the proposed algorithms.