In this paper, experimental investigation on 1 kW fiber laser cutting carbon fiber composite materials is carried out. The influence of laser power, cutting speed, and assistant gas pressure on the slit width, the heat-affected zone and the slit taper is studied using single factor method. Orthogonal experiments are used to study the main factor that affect the width of the slit and the width of the heat-affected zone. The results show that the slit width, notch taper and heat-affected zone increase with the increasing of laser power. With the cutting speed increasing, the width of the slit and the heat-affected zone decreased, and the notch taper increased first and then decreased. With the increase of the assistant gas pressure, the slit width and the taper of the incision increased, and the width of the heat affected zone decreased. When the laser power, the cutting speed, and the assistant gas pressure is 100 W, 1 m/min, and 0.5 MPa respectively, the cutting quality is better, and the cutting efficiency is higher.