We propose a type system for the Java bytecode language, prove the type soundness, and develop a type inference algorithm. In contrast to the existing proposals, our type system yields a typed term calculus similar to type systems of lambda calculi. This enables us to transfer existing techniques and results of type theory to a JVM-style bytecode language. We show that ML-style let polymorphism and recursive types can be used to type JVM subroutines, and that there is an ML-style type inference algorithm. The type inference algorithm has been implemented. The ability to verify type soundness is a simple corollary of the existence of type inference algorithm. Moreover, our type theoretical approach opens up various type safe extensions including higher-order methods, flexible polymorphic typing through polymorphic type inference, and type-preserving compilation.