We introduce the notion of Krein-operator convexity in the setting of Krein spaces. We present an indefinite version of the Jensen operator inequality on Krein spaces by showing that if (H,J) is a Krein space, U is an open set which is symmetric with respect to the real axis such that U∩R consists of a segment of real axis and f is a Krein-operator convex function on U with f(0)=0, then f(C^#AC)≦^JC^#f(A)C for all J-positive operators A and all invertible J-contractions C such that the spectra of A, C^#AC and D^#AD are contained in U, where D is a defect operator for C^#. We also show that in contrast with usual operator convex functions the converse of this implication is not true, in general.