COE-4 zeolites possess a unique two-dimensional ten-ring pore structure with the Si(OH)2 hydroxyl groups attached to the linker position between the ferrierite-type layers, which has been demonstrated through the interlayer-expansion approach in our previous work (H. Gies et al. Chem. Mater. 2012, 24, 1536). Herein, density functional theory is used to study the framework stability and Brønsted acidity of the zeolite T-COE-4, in which the tetravalent Si is isomorphously substituted by a trivalent Fe, B, Ga, or Al heteroatom at the linker position. The influences of substitution energy and equilibrium geometry parameters on the stability of T-COE-4 are investigated in detail. The relative acid strength of the linker position is revealed by the proton affinity, charge analysis, and NH3 adsorption. It is found that the range of the 〈T-O-Si〉 angles is widened to maintain the stability of isomorphously substituted T-COE-4 zeolites. The smaller the 〈O1-T-O2〉 bond angle is, the more difficult is to form the regular tetrahedral unit. Thus, the substitution energies at the linker positions increase in the following sequence: Al-COE-4 < Ga-COE-4 < Fe-COE-4 < B-COE-4. The adsorption of NH3 as a probe molecule indicates that the acidity can affect the hydrogen-bonding interaction between (NH⋅⋅⋅O2) and (N⋅⋅⋅HO2). The relative Brønsted-acid strength of the interlayer-expanded T-COE-4 zeolite decreases in the order of Al-COE-4 > Ga-COE-4 > Fe-COE-4 > B-COE-4. These findings may be helpful for the structural design and functional modification of interlayer-expanded zeolites.