LetM 2n+1 (c) be (2n + 1)-dimensional Sasakian space form of constant ϕ-sectional curvature c and M n be an n-dimensional C-totally real minimal submanifold ofM 2n+1 (c). If M n is semi-parallel and the sectional curvature of M n is greater than (n−2)(c+3) 4(2n−1) , then M n is totally geodesic. Then we prove that a C-totally real minimal surface of a 5-dimensional Sasakian manifoldM (c) with constant ϕ-sectional curvature c, if M is semi-parallel surface, then M is totally geodesic or flat.