In clinical anesthesia and the rescue of critically ill patients, arterial puncture and catheterization are the most commonly chosen ways to establish central arterial access for patients. Invasive arterial puncture and catheterization facilitate the grasp of real-time vital sign information of patients during surgery, which strengthens patient monitoring during surgery and improves safety. However, the traditional method of arterial puncture and cannulation through palpation of the radial artery is often prone to complications related to mechanical injury, such as hemorrhage, hematoma, and accidental perforation of the artery. Studies have shown that ultrasound-guided radial artery puncture and cannulation can shorten the puncture cannulation time, reduce the incidence of complications related to puncture cannulation, and improve the success rate of puncture cannulation. In order to verify it, this paper uses the experimental group and the control group to conduct comparative experiments and uses the neural network method to evaluate the effects of the two methods. As a more mature method of artificial intelligence, BP neural network is widely used in a wide range of applications and has the characteristics of strong generalization ability and fast convergence, so we choose it as the base model. The specific work of this paper is as follows: (1) in-depth study of the relevant theory of BP neural network (BPNN), focusing on the structure of BPNN and the working principle of algorithm; the problems to be solved in the clinical anesthesia effect evaluation have laid a theoretical foundation for the establishment of an improved BPNN evaluation model in the following chapters. (2) introduce the basic principle of genetic neural network, analyze the benefits of combining genetic neural network and BPNN; introduce in detail the process of genetic algorithm to optimize the weights and thresholds of BPNN, and establish a GA-BP evaluation model. The test proves the feasibility and superiority of the model.