The invention relates to the technical field of alkylation catalyzed by acidic polymerized ionic liquids, and particularly relates to a method of preparing alkylate oil by utilizing a Lewis acid based acidic polymerized ionic liquid catalyst. A polymerized ionic liquid acidified by adopting a Lewis acid is adopted as the catalyst of the method, and a continuous catalytic liquid-phase butane/butylenes alkylation reaction is performed at 20-200 DEG C by adopting a fixed bed reactor. The catalyst is easy to prepare, durable in activity, convenient to regenerate and free of generation of waste acids, thus achieving green alkylation.