In order to realize non-vertical laser cutting of polymer materials, a non-vertical laser cutting model is established. The change laws of kerf width and heat affected zone (HAZ) width with the laser line energy, the incident angle and the defocusing amount are obtained by solving the threshold value energy equation. In the continuous CO2 laser cutting system, the cutting experiment is done on polyethylene terephthalate (PET) film with the orthogonal experimental method. It is found that the kerf width and the HAZ width change gently and the cutting quality is good when the incident angle is in the range of -57.3° to 57.3° and the defocusing amount is in the range of -15 mm to 15 mm. The results show that this model can accurately predict kerf width and HAZ width in non-vertical laser cutting of polymer materials, which provides parameter guidance in laser cutting of complex films with curved faces.