Among the various zeolite membranes, hydrophilic Linde Type A (LTA) zeolite membranes (LTA membranes) are highly desirable for the dehydration of organic solvents. In particular, both high flux and separation factors for H₂O can be achieved with such membranes. Therefore, in this study, we fabricated LTA membranes on thin-walled capillary tubes and compared the dehydration performance with those of LTA membranes prepared on conventional tubular supports. We found that neither LTA membrane contained noticeable defects using fluorescence confocal optical microscopy analysis. Accordingly, both membranes effectively dehydrated an azeotropic ternary mixture of H₂O/isopropanol (IPA)/epichlorohydrin (ECH), an industrially important mixture. Specifically, the capillary-supported LTA membrane showed better dehydration performance than that on the conventional tubular support, mainly because of the relatively thinner support thickness (ca. 0.35 mm vs. 2 mm of the conventional tubular support). The corresponding H₂O flux was ca. 8.02 ± 0.94 kg·m^-2·h^-1 for the azeotropic ternary mixture (20 wt% H₂O/30 wt% IPA/50 wt% ECH) at 70 °C (vs. 4.26 ± 0.39 kg·m^-2·h^-1 through the LTA membrane on the conventional tube). Further, the H₂O/IPA and H₂O/ECH separation factors exceeded approximately 10,000. Finally, a comparison with the literature data revealed that the capillary-supported LTA membrane had higher H₂O flux and selectivity for H₂O/IPA mixtures than other LTA membranes prepared on conventional discs/sheets/tubes.