We consider a simple Higgs portal dark-matter model, where the standard model is supplemented with a complex scalar whose imaginary part plays the role of weakly interacting massive particle dark matter (DM). We show that the direct DM detection cross section vanishes at the tree level and zero momentum transfer due to a cancellation by virtue of a softly broken symmetry. This cancellation is operative for any mediator masses. As a result, our electroweak-scale dark matter satisfies all of the phenomenological constraints quite naturally.