The measurement of the flux-integrated cross-sections on $\rm{H_{2}O}$ and CH using the T2K anti-neutrino beam is reported. The signal is defined as the charged-current interaction with one induced muon and no detected charged-pion nor proton. The phase spaces of muons are restricted to $p_{\mu}>0.4~{\rm MeV}/c$ and $\theta_{\mu}<30~\rm{degrees}$, in the laboratory frame. In addition, detectable phase spaces of pions and protons are defined as $p_{\pi}>0.2~{\rm MeV}/c$ and $\theta_{\pi}<70~\rm{degrees}$, and $p_{\rm p}>0.6~{\rm MeV}/c$ and $\theta_{\rm p}<70~\rm{degrees}$, respectively. No pions nor protons are required in these regions. Both of the $\bar{\nu}_{\mu}$ cross-sections and $\bar{\nu}_{\mu} + \nu_{\mu}$ cross-sections on $\rm{H_{2}O}$ and CH targets, and their ratios are measured. The results of $\bar{\nu}_{\mu}$ cross-section measurements are $\sigma_{\rm H_{2}O}\,=\,(1.082\pm0.068(\rm stat.)^{+0.145}_{-0.128}(\rm syst.)) \times 10^{-39}~{\rm cm^{2} / nucleon}$, $\sigma_{\rm CH}\,=\,(1.096\pm0.054(\rm stat.)^{+0.132}_{-0.117}(\rm syst.)) \times 10^{-39}~{\rm cm^{2} / nucleon}$, and $\sigma_{\rm H_{2}O}/\sigma_{\rm CH} = 0.987\pm0.078(\rm stat.)^{+0.093}_{-0.090}(\rm syst.)$, and those of $\bar{\nu}_{\mu} + \nu_{\mu}$ cross-section measurements are $\sigma_{\rm H_{2}O} = (1.155\pm0.064(\rm stat.)^{+0.148}_{-0.129}(\rm syst.)) \times 10^{-39}~{\rm cm^{2} / nucleon}$, $\sigma_{\rm CH}\,=\,(1.159\pm0.049(\rm stat.)^{+0.129}_{-0.115}(\rm syst.)) \times 10^{-39}~{\rm cm^{2} / nucleon}$, and $\sigma_{\rm H_{2}O}/\sigma_{\rm CH}\,=\,0.996\pm0.069(\rm stat.)^{+0.083}_{-0.078}(\rm syst.)$.