In solid-state alkaline fuel cells (SAFCs), water is generated at the anode and is reacted at the cathode; as such, flooding occurs much more easily at the anode than it does in proton-exchange membrane fuel cells (PEMFCs). Anode flooding is a reason for the low performance of SAFCs, and so it is important that this flooding phenomenon is mitigated. In this study, we control water transport to suppress anode flooding. We do this through two approaches: changing the thickness of the anion exchange membrane (AEM) and changing the anode flow rate. Among two AEMs with two different thicknesses (27 μm and 6 μm) prepared, thinner AEM shows improved fuel cell performance. Increasing the anode flow rate also improved the performance of SAFCs. To find out what caused this, the water transport inside the membrane electrode assembly (MEA) was analyzed. The flooding region was estimated using calculated relative humidity at anode outlet. On the basis of our experimental and calculation approaches, flooding can be suppressed by using thin AEMs and increasing the anode flow rate.