  The spin-$\frac{1}{2}$ delta-chain (sawtooth chain) with antiferromagnetic
Heisenberg basal chain and Ising apical-basal interactions is studied. The
basal-apical interactions involve the bond alternation. The limiting cases of
the model include the symmetrical delta-chain and the antiferromagnetic chain
in the staggered magnetic field. We study ground state properties of the model
by the exact diagonalization and density matrix renormalization group methods.
The ground state phase diagram as a function of the bond alternation consists
of magnetic and various non-magnetic phases. All phases excluding the
ferrimagnetic phase are gapped and an origin of the gaps is cleared.
