The extensive applications of multi-function radars (MFRs) have presented a great challenge to the technologies of radar countermeasures (RCMs) and electronic intelligence (ELINT). The recently proposed cognitive electronic warfare (CEW) provides a good solution, whose crux is to perceive present and future MFR behaviours, including the operating modes, waveform parameters, scheduling schemes, etc. Due to the variety and complexity of MFR waveforms, the existing approaches have the drawbacks of inefficiency and weak practicability in prediction. A novel method for MFR behaviour recognition and prediction is proposed based on predictive state representation (PSR). With the proposed approach, operating modes of MFR are recognized by accumulating the predictive states, instead of using fixed transition probabilities that are unavailable in the battlefield. It helps to reduce the dependence of MFR on prior information. And MFR signals can be quickly predicted by iteratively using the predicted observation, avoiding the very large computation brought by the uncertainty of future observations. Simulations with a hypothetical MFR signal sequence in a typical scenario are presented, showing that the proposed methods perform well and efficiently, which attests to their validity.