The absorption characteristics of a grapheme cavity in a one-dimensional periodic structure are studied by using a transfer matrix method. The variation of the absorption frequency and absorption peaks in the waveband from 700 nm to 950 nm is analyzed by changing the size of different media, the incident angle and the electromagnetic wave mode. The result shows that single frequency or two frequency peaks may be produced when the thickness of the defect layer is changed. The variation of the incident angle and electromagnetic wave mode has a greater influence on the values of absorption peaks. The result may provide theoretical basis for the design of near infrared grapheme absorbers.