The catalytic activity of SiO2–ZrO2 mixed oxides was studied for the Friedel–Crafts-alkylation reaction between anisole and benzylic or allylic alcohols. In particular, the influence of Zr content on the catalytic activity was studied. The catalyst with the lowest Zr content (5 mol % ZrO2) showed the highest activity with high selectivity for the alkylated product and good recyclability. We used this catalyst in the reaction of 1-phenyl-1-ethanol with toluene and xylene. We also studied the possibility of a tandem process that involved a Friedel–Crafts alkylation and the subsequent trans-hydrogenation of trans-1,3-diphenyl-2-propen-1-ol for the synthesis of substituted cyclopropanes.