Abstract: Maximum Satisfiability problem (MaxSAT) is a classic optimization problem and NP-hard problem. Many NP problem can be transformed into MaxSAT problem, and many industrial problems are solved by MaxSAT algorithms effectively. Improved technologies and data structure proposed in recent years lad to solve much larger instance than before. The design of MaxSAT exact algorithm based on branch and bounds used inference rules and failed literal detection to reduce the running time. Inference rules proposed in the past time obeyed the equivalence of MaxSAT problem. Compared to not using inference rules, new clauses in clause set created by inference rules can deduce more conflict sets and improve binary tree pruning rate and algorithm’s performance. Inference rules fund equivalent clauses for chain structure or cycle structure of conflict clause set. Through the analysis of cycle conflict set whose step length is greater than 2, find the new equivalent clause sets with them. The equivalent proof about new clause sets and conflict sets was described in this article. Therefore, new cycle extend inference rules were proposed to improve lower bounds and reduce the running time in further. Integer programming proved the soundness of new cycle extend inference rule. New algorithm Maxsatce algorithm adopted new rules and worked on the base of Maxsatz2013. Experiments tested four types MaxSAT instances from the website of MaxSAT competition. The experimental results showed cycle extend inference rules could improve the lower bounds at binary tree branch when solving instance’s clause length was greater than or equal to 3. Experiment result showed cycle extend inference rule can work well when search level was close to middle of search tree. Running time of random instances and crafted instances can reduce at least 3% ~14%.