Abstract: For totally real complete space-like submanifolds in indefinite complex space form, the problem of establishing geometric inequalities between the intrinsic invariants δ (n₁, n₂, …, n_k) and the extrinsic invariants (square of the mean curvature) was studied. The inequalities about δ(2) and δ(n₁, n₂, …, n_k) of time-like and space-like geodesic submanifolds in the indefinite complex space were established by algebraic inequalities and moving frame methods, and the δinequality for totally real complete space-like submanifolds in indefinite complex space form was obtained.