With the liberation of the electricity market, a growing number of investors participate in market bidding. However, due to the inaccurate prediction of wind power, the interest of the investors can be damaged. In order to solve such problem, a distributionally robust chance-constrained (DRCC) scheduling for a wind-battery hybrid system in the day-ahead electricity market is developed by considering the uncertain wind power. The overall objectives of this paper contain revenue calculation from the electricity market, curtailment penalty caused by the wind power, and degradation cost of the battery. When selling/buying electricity is to/from the electricity market, the available power is limited by the capacity of the transmission line. This paper develops a chance constraint for the transmission line and introduces the moment ambiguity set to capture the uncertain wind power generation. The chance constraint can be reformulated into a standard second-order conic programming problem (SOCP) via a distributionally robust optimization method. The model is tested with a case study and the results indicate that the battery plays an important role in wind power scheduling in the electricity market. In the end, comparison with the stochastic optimization with normal distribution (SND) is conducted to prove the performance and robustness of the proposed model based on a distributionally robust optimization (DRO) method.