We propose a method of association rule mining using genetic network programming (GNP) with time series processing mechanism and attribute accumulation mechanism in order to find time related sequence rules efficiently in association rule extraction systems. We suppose that, the database consists of a large number of attributes based on time series. In order to deal with databases which have a large number of attributes, GNP individual accumulates better attributes in it gradually round by round, and the rules of each round are stored in the Small Rule Pool using hash method, and the new rules will be finally stored in the Big Rule Pool. The aim of this paper is to better handle association rule extraction of the database in many time-related applications especially in the traffic prediction problem. In this paper, the algorithm capable of finding the important time related association rules is described and experimental results considering a traffic prediction problem are presented.