Influenza rapidly spreads in seasonal epidemics and imposes a considerable economic burden on hospitals and other healthcare costs. Thus, predicting the propagation of influenza accurately is crucial in preventing influenza outbreaks and protecting public health. Most current studies focus on the spread simulation of influenza. However, few studies have investigated the dependencies between meteorological variables and influenza activity. This study develops a non-parametric model based on Gaussian process regression for influenza prediction considering meteorological effect to capture temporal dependencies hidden in influenza time series. To identify the most explanatory external variables, L1-regularization is applied to identify meteorology factor subsets, and three types of covariance functions are designed to characterize non-stationary and periodic behavior in influenza activity. The dependencies of diseases and meteorology are modeled through the designed cross-covariance function. A real case in Shenzhen, China was studied to validate our proposed model along with comparisons to recently developed multivariate statistical models for influenza prediction. Results show that our proposed influenza prediction approach achieves superior performance in terms of one-week-ahead prediction of influenza-like illness.