The effective one-body method provides a framework to apply the black hole perturbation theory to the binary system where two masses can be comparable. We study the gravitational-wave equation in the background of the effective one-body system for the spinless binary, which is in general available with the spherically symmetric background as well. We obtain the gauge conditions for the decoupled wave equation, and also give the solutions to the gauge conditions in terms of the metric perturbation for a special case, which extends the result by Jing et al. (Sci. China-Phys. Mech. Astron. 65, 26...