We classify irreducible Whittaker modules for generalized Heisenberg Lie algebra t and irreducible Whittaker modules for Lie algebra t obtained by adjoining m degree derivations d1, d2, . . . , dm to t. Using these results, we construct imaginary. Whittaker modules for non-twisted extended affine Lie algebras and prove that the imaginary Whittaker modules of Z-independent level are always irreducible.