Abstract: Constructs the differential manifold of stock return process based on information geometry,and gives its geometric structure such as the Fisher metric matrix and α-connection coefficients.The Gauss curvature and α-geodesic of the manifold are obtained in the sense of corresponding α-connection.Solution of the geodesic equation when α=0 is thereby given.Also the α-divergence,α-Kullback divergence and J-divergence of the manifold are given,whilst the relation between the α-divergence and α-Kullback divergence are shown and the divergences in some special cases are given too.