  Using the bosonization and level spectroscopy methods, we study the
ground-state phase diagram of a XXZ antiferromagnet on a railroad-trestle
lattice with asymmetric leg interactions. It is shown that the asymmetry does
not change the dimer/Neel transition line significantly, which agrees with the
expectation based on a naive bosonization procedure, but it does change the
dimer/spin-fluid transition line. To understand this observation, we analyze
eigenvectors of the ground state, dimer excitation, doublet excitation and Neel
excitation, and find that only the doublet excitation is affected by the
asymmetric interaction.
