Time series has a wide range of applications in various fields. Recently, a new math tool, named as visibility graph, is developed to transform the time series into complex networks. One shortcoming of the existing network-based time series prediction methods is time consuming. To address this issue, this paper proposes a new prediction algorithm based on visibility graph and Markov chains. Among the existing network-based time series prediction methods, the main step is to determine the similarity degree between two nodes based on link prediction algorithm. A new similarity measure between two nodes is presented without the iteration process in the classical link prediction algorithm. The experiments show that the proposed method has better accuracy with less time consuming.