Neighborhood rough sets based attribute reduction, as a common dimension reduction method, has been widely used in machine learning and data mining . Each attribute has the same weight (the degree of importance) in the existing neighborhood rough set models. In this work, we introduce different weights into neighborhood relations and propose a novel approach for attribute reduction. The main motivation is to fully mine the correlation between attributes and decisions before calculating neighborhood relations, and the attributes with high correlation are assigned higher weights. We first construct a Weighted Neighborhood Rough Set (WNRS) model based on weighted neighborhood relations and discuss its properties. Then WNRS based dependency is defined to evaluate the significance of attribute subsets. We design a greedy search algorithm based on WNRS to select an attribute subset which has both strong correlation and high dependency. Furthermore, we use isometric search to find the optimal neighborhood threshold. Finally, ten datasets from UCI machine learning repository and ELVIRA Biomedical data set repository are used to compare the performance of WNRS with those of other state-of-the-art reduction algorithms. The experimental results show that WNRS is feasible and effective, which has higher classification accuracy and compression ratio.