In this note, we introduce a notion of the J -kernel of a bounded linear operator on a Krein space and study the J -Fredholm theory for Krein space operators. Using J -Fredholm theory, we discuss and study the J -essential pseudospectra of bounded linear operators on Krein spaces, and some of their properties are studied. Furthermore, we discuss the structure of the J -essential pseudospectra of infinite-dimensional Hamiltonian operators.