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Traditionally, network risk assessment uses a statistical computation method. This paper proposes Lie group kinematics to describe the feature space of the attack behavior. A matrix composed of indicators and topologies in a network system is mapped to a Lie group. The attack behavior path and the powers of the attack and defense are defined. The risk value of the attack and defense is calculated from the change in the indicators. Then, we evaluate the network security risk status using calculus. To examine the validity of the network risk assessment based on a Lie group, we conduct one experiment and utilize the CIC2017 dataset to show the applicability and efficiency of the proposed method. The experimental results show the effectiveness of the calculation method based on a Lie group, and the risk value of the attack and defense is valid compared to those of other machine learning algorithms. The calculation method based on a Lie group can quantitatively analyze network security risks..