We present a theory of magnetoplasmons in tunneling semiconductor superlattices. A new magnetoplasmon branch is predicted as a consequence of the electron tunneling in the superlattice direction. Explicit analytical results for the dispersion relation of the tunneling magnetoplasmon branch are derived in an effective-mass-like approximation, and also in a tight-binding approximation which takes into account the umklapp effects in the superlattice direction. The tunneling magnetoplasmon branch should be experimentally observable.