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This paper addresses the global stability analysis of the SEIRS epidemic model with a nonlinear incidence rate function according to the Lyapunov functions and Volterra-Lyapunov matrices. By creating special conditions and using the properties of Volterra-Lyapunov matrices, it is possible to recognize the stability of the endemic equilibrium (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>E</mi><mn>1</mn></msub></semantics></math></inline-formula>) for the SEIRS model. Numerical results are used to verify the presented analysis.