The generalized estimating equations (GEE) method is a popular approach for analyzing dependent data of various types. While GEE estimators are robust against the misspecification of the correlation matrix, their estimation efficiency can be seriously affected by the choice of the working correlation matrix.For spatially correlated data, it is difficult to specify the true spatial correlation structure due to the complexity of dependence and the high dimension of spatial correlation matrices. To achieve estimation efficiency while allowing flexibility to capture complex spatial dependence, we propose a new GEE-type approach based on a mixture of spatial working correlation matrices, referred to as mix-GEE. We show that the mix-GEE estimator is asymptotically efficient without any parametric assumption on the distribution as long as one of the candidate