Accurate short-term load prediction is advantageous to enhance the secure and economic effect of electric system and ameliorate the supply quality. Thus, it is important to find an effective method to improve the short-term forecast precision effectively. There are lots of uncertain factors in smart grid power system affect the accuracy of the load forecasting directly. Meanwhile some less important factors can be reduced by attribute reduction. In this paper, association rule analysis is proposed to analyze the relevance of power load and its influencing factors, in order to improve the accuracy of load forecasting, and reduce the operation time. In this paper, a new method (FNNAR) is presented to forecast short-term load which is based on Association Rules (AR) and Fuzzy Neural Network (FNN). The Association Rules Mining algorithm based on Quantitative Concept Lattice (ARMQCL) is proposed to extract association rules. And attribute reduction is carried out based on these extracted association rules. Finally, FNN model uses the reduced attributes as the input to forecast the electric load in smart grid. Experimental results indicate that the proposed forecast method (FNNAR) has higher accuracy and less running time.