A spring-damping contact force model considering the normal friction force is proposed and discussed in this paper. This model is an extension and development of Hertz theoretical model. The physical model of contact force in the contact process is established. The friction force during the elastic compression and restitution phases is represented using the product of tangential component of contact force and friction coefficient, which is a function of contact force and deformation. The friction dissipation coefficient is proposed to characterize the energy dissipation under different material properties and initial velocities. A velocity exponential model is proposed, and the expressions of damping coefficient and contact force are derived. Numerical analysis is carried out and the model in this paper is compared with classical models under two conditions, which proves the correctness and effectiveness of the model. The spring-damping model with normal friction force is applied to a simple spring contact system, and the energy dissipation process under the action of spring prestress is analyzed.