In　order　to　alleviate　the　computational　burden　of　large　CNN　(convolutional　neural　network)　models　in　current　face　verification　systems,　convolution　theorem　was　proposed,　which　suggested　that　convolution　in　the　spatial　domain　was　equivalent　to　product　in　the　frequency　domain,　to　speed　up　the　convolutional　layers　in　CNN,　and　consequently　accelerate　face　verification　systems.　By　transforming　time-consuming　convolutions　into　product　operations　in　the　frequency　domain,　much　computation　was　saved　without　loss　of　accuracy.　The　computational　complexities　of　convolution　by　using　the　convolution　theorem　and　the　direct　computation　were　compared,　and　the　conditions　under　which　acceleration　can　be　achieved　by　convolution　theorem　were　given.　After　Fourier　transform,　the　way　of　fulfillment　of　the　product/sum　operations　in　parallel　was　explored　in　detail,　with　the　goal　to　fully　utilize　the　power　of　GPU　(graphics　processing　unit).　Results　show　that　the　proposed　algorithm　has　achieved　apparent　speedups　for　some　recent　face　verification　models,　demonstrating　its　effectiveness.　©　2017,　Editorial　Department　of　Journal　of　Beijing　University　of　Technology.　All　right　reserved.