  We study the one-dimensional quarter-filled extended Hubbard model with an
alternating transfer integral. In the strong-dimerization limit the charge part
is described by the quantum Ising model which shows the two-dimensional Ising
criticality at the self-dual point, and it is naturally connected to the
double-frequency sine-Gordon theory in the weak dimerization. Treating
low-lying excitations in finite-size systems, we numerically determine a phase
boundary between two types of $4k_{\rm F}$ density-wave states and clarify the
ground-state phase diagram. Further, we refer to its relevances to the
charge-ordered phase observed in the charge-transfer organic salts.
