In this paper,the authors introduce a class of functionals.This class forms a Banach algebra for the special cases.The main purpose of this paper is to investigate some properties of the modified analytic function space Feynman integral of functionals in the class.Those properties contain various results and formulas which were not obtained in previous papers.Also,the authors establish some relationships involving the first variation via the translation theorem on function space.In particular,the authors establish the Fubini theorem for the modified analytic function space Feynman integral which was not obtained in previous researches yet.