The invention present invention belongs to waste polyester recycling technology field and relates to a method and a device for recycling waste polyester, in particular to a method and a device for recycling waste polyester by modified chemical method to recover waste polyester to prepare dimethyl terephthalate (DMT). The recycling method of the present invention uses a process of continuous feeding, continuous alcoholysis and continuous transesterification. It can make the material undergo homogeneous alcoholysis in the melted state, and the required alcoholysis time is short. Because more than two alcoholysis tanks are used in series for continuous alcoholysis, the product quality of alcoholysis product is stable. When the alcoholysis product is continuously transesterified, it avoids the occurrence of side reactions and the unstable quality of the transesterified product, and the purity and yield of recycling product of waste polyester are greatly improved.