Herein, we have developed a continuous-process for the direct cyclopropanation of various alkenes nonconjugated with carbonyl using trimethylsulfoxonium iodide as a methylene source via the Corey–Chaykovsky cyclopropanation reaction in the presence of Amberlyst-A26 as a heterogeneous base. Several 9-alkylidene-9H-fluorene derivatives successfully undergo Corey–Chaykovsky cyclopropanation to afford spiro[cyclopropane-1,9′-fluorene] in excellent yields under the continuous-process module. Furthermore, continuous process for the cyclopropanation of 3-benzylideneindolin-2-one derivatives using Amberlyst-A26 as a heterogeneous base has been described, which afford spiro[cyclopropane-1,3′-indolin]-2′-one derivatives.