Exception handling is an important and difficult part of the Java programming’s teaching and training. The paper points out and discusses the two outstanding problems in details during teachings, that are how can make students master exactly the basic ideas of exception handling and locations need to be handled by exception handling methods in Java programs. Furthermore proposes a kind of teaching process which gradually shows the puzzles during the learning of students starting from the case by combining the heuristic teaching with the practical case of significance, and figures out step by step the solving methods, namely the knowledge points, which have to be learned about exception handling. Visualization and simplification are their advantages, which facilitates the students’ learning and understanding. The teaching practice shows that the good teaching results have been achieved.