  We make a matrix-product variational approach to spin-1/2
ferromagnetic-antiferromagnetic bond-alternating chains with anisotropy on
their ferromagnetic bonds, especially under the open boundary condition. The
rich phase diagram containing the Haldane, large-D, and two types of Neel
phases is well reproduced with only two variational parameters. The on-bond
anisotropy has a significant effect on the ferromagnetic coupling between
neighboring spins and induces novel edge states peculiar to spin-1/2 chains.
