The maximum independent set problem is a basic NP-hard problem and has been extensively studied in exact algorithms. The maximum independent set problems in low-degree graphs are also important and may be bottlenecks of the problem in general graphs. In this paper, we present a 1.173 6 n n O ( 1 ) -time exact algorithm for the maximum independent set problem in an n -vertex graph with degree bounded by 5 , improving the previous running time bound of 1.189 5 n n O ( 1 ) . In our algorithm, we show that the graph after applying reduction rules always has a good local structure branching on which will effectively reduce the instance. Based on this, we obtain an improved algorithm without introducing a large number of branching rules.