Web sequential patterns are important for analyzing and understanding users behaviour to improve the quality of service offered by the World Wide Web. Web Prefetching is one such technique that utilizes prefetching rules derived through Cyclic Model Analysis of the mined Web sequential patterns. The more accurate the prediction and more satisfying the results of prefetching if we use a highly efficient and scalable mining technique such as the Bidirectional Growth based Directed Acyclic Graph. In this paper, we propose a novel algorithm called Bidirectional Growth based mining Cyclic behavior Analysis of web sequential Patterns (BGCAP) that effectively combines these strategies to generate prefetching rules in the form of 2-sequence patterns with Periodicity and threshold of Cyclic Behaviour that can be utilized to effectively prefetch Web pages, thus reducing the users perceived latency. As BGCAP is based on Bidirectional pattern growth, it performs only (log n+1) levels of recursion for mining n Web sequential patterns. Our experimental results show that prefetching rules generated using BGCAP is 5-10 percent faster for different data sizes and 10-15% faster for a fixed data size than TD-Mine. In addition, BGCAP generates about 5-15 percent more prefetching rules than TD-Mine.