This paper primarily addresses the distributed online stochastic optimization problem where the objective functions are assumed to be non-convex and the sequence of objective functions is non-stationary. We propose a distributed one-point residual feedback (ORF) algorithm to solve the online stochastic optimization problem. Then the regret bounds of proposed algorithm is analysed under the assumption that the local objective functions are Lipschitz or smooth, which implies that the regret is sublinearly increasing. The conclusion shows that the proposed algorithm can solve the distributed online stochastic problems more effective and has lower variance than traditional one-point feedback method in estimating the unknown gradient of objective function.