In this paper, we propose a novel deep sequence model based on the Koopman theory for time series forecasting with distribution shifts. Our model, Koopman Neural Forecaster (KNF), leverages DNNs to learn the linear Koopman space and the measurement functions, and imposes inductive biases for improved robustness against distributional shifts. KNF employs both a global operator to learn shared characteristics, and a local operator to capture changing dynamics. KNF also includes a judiciously-designed feedback loop to continuously update the learnt operators over time for rapidly varying behaviors. To the best of our knowledge, this is the first time that Koopman theory is applied to real-world time series without known governing laws. We demonstrate that KNF achieves the state-of-the-art performance on wide range of time series datasets that are particularly known to suffer from distribution shifts.