With development of economy, all industries have undergone earthshaking changes. Various new technologies are starting to be employed in all aspects of life, and graphic design is no exception. The use of computer graphics and image processing technologies in graphic design can substantially improve design efficiency and make graphic design job more convenient to develop. The requirements for the quality of graphic design are higher. Quality inspection has become a necessary step in the production process, in which the detection of graphic design defects is an indispensable and important link. The traditional graphic design defect detection adopts the method of manual visual inspection, which has the disadvantages of poor stability, long consumption time, and high labor cost. As an efficient computer graphics and image processing technology, convolutional neural network has received extensive attention in graphic design defect detection because of its advantages of high speed, efficiency, and high degree of automation. Taking agricultural product packaging as an example, this paper studies application technology for graphic design defect detection with convolutional neural network (CNN). The main contents are as follows: construct the original YOLOv3 network model, input the graphic design images of agricultural product packaging into the network model in batches according to the computing power of the hardware equipment, train the YOLOv3 network, and deeply study and analyze the experimental results. The related improvement techniques are then given, based on the characteristics of agricultural product packaging design faults. The backbone network, multiscale feature map, a priori frame, and activation function of YOLOv3 are improved, and then performance of the improved model is verified by experiments.