The analysis of software system evolution is highly significant in software research as the evolution runs throughout the lifecycle of a software system. Considering a software system as an algebraic engineering system, we propose a software system evolution analysis method based on algebraic topology. First, from a complex network perspective, we abstract a software system into the software structural topology diagram. Then, based on the algebraic topology principle, we abstract each node in the software structural topology diagram into an algebraic component represented by a 6-tuple. We propose three kinds of operation relationships between two algebraic components, so that the software system can be abstracted into an algebraic expression of components. In addition, we propose three forms of software system evolution, which help to analyze the structure and evolution of system software and facilitate its maintenance and reconfiguration.