Composition formula is one of the most important research topics in functional analysis theory. Various relationships can be obtained using the composition formula. Since the generalized Brownian motion process used in this paper has a non-zero mean function, there are many restrictions on obtaining a composition formula for the modified analytic function space Fourier–Feynman transform. This paper contains an idea of how the composition Formula (9) below is established for the modified analytic function space Fourier–Feynman transform on function space. Using this idea, we are able to solve a problem that had never been solved before.