• CoMo/δ-Al 2 O 3 had the highest HDS activity while CoMo/θ-Al 2 O 3 showed the highest HDS selectivity. • The selectivity factor was proportional to the edge-to-corner ratio of CoMoS slabs (f e / f c) CoMo. • The large pores of θ-Al 2 O 3 was beneficial for weakening the internal diffusion resistance. • The θ-Al 2 O 3 was an ideal carrier to prepare industrial catalysts in the selective HDS of FCC naphtha. To achieve a high desulfurization degree while minimizing the olefin hydrogenation (HYD) is the biggest challenge in the selective hydrodesulfurization (HDS) of fluid catalytic cracking (FCC) naphtha. In this work, alumina with different crystal phases (γ-Al 2 O 3 , δ-Al 2 O 3 and θ-Al 2 O 3) were utilized as carriers to prepare CoMo/Al 2 O 3 selective HDS catalysts. The influence of alumina crystal phase on the morphology of active phase and catalytic performance of their corresponding CoMo/Al 2 O 3 catalysts has been studied in detail. It was found that CoMo/δ-Al 2 O 3 showed the highest HDS activity due to an appropriate weakened metal-support interaction and the modest Mo dispersion. However, CoMo/θ-Al 2 O 3 showed a much higher HDS selectivity than that of CoMo/γ-Al 2 O 3 and CoMo/δ-Al 2 O 3. The significantly enhanced HDS selectivity was attributed to a notably larger edge-to-corner ratio of CoMoS slabs (f e / f c) CoMo , thus resulting in a slightly reduction of HDS activity while a significantly decreased olefin HYD activity. Besides, the large pores of θ-Al 2 O 3 are beneficial for weakening the internal diffusion resistance when utilizing full-size catalysts. Therefore, θ-Al 2 O 3 is an ideal carrier to prepare the industrial CoMo/Al 2 O 3 catalysts for the HDS of FCC naphtha. [ABSTRACT FROM AUTHOR]