Summary: Although various innovative sensing technologies have been widely employed, data missing in collections of time series occurs frequently, which turns out to be a major menace to precise data analysis. However, many existing missing data prediction approaches either might be infeasible or could be inefficient to predict missing data from multiple time series. To solve this problem, we proposed a novel approach based on the compressive sensing theory and sparse Bayesian learning theory for missing data prediction in coevolving time series. First, we model the problem by designing the corresponding sparse representation basis and measurement matrix. Then, the missing data prediction problem is formulated as the multiple sparse vectors recovery problem. Many simultaneous sparse estimation approaches focus on joint estimation of multiple sparse vectors with a common support from given linear observations, which is however too strict in some real applications. In this paper, largely utilizing the interior patterns of coevolving time series, we design a tuning parameter-free algorithm based on the sparse Bayesian learning, which can simultaneously solve multiple sparse estimation takes without the requirement of auxiliary information. Simulation results demonstrate that our approach can recover the entire time series efficiently using only those data that are not missing, even if, a high ratio of collected data are missing.