J. C. Maxwell applied the quaternion analysis to describe the electromagnetic theory. While A. Einstein depicted the gravitational theory by means of the tensor analysis and curved Four-spacetime. At present the scholars research the electromagnetic and gravitational features, making use of the complex-quaternion/octonion curved space. It is capable of defining the parallel translation and covariant derivative of the complex-octonion curved space, by means of the orthogonality of two complex octonions, depicting simultaneously the electromagnetic and gravitational features in the complex-octonion curved space. The study reveals that the connection coefficient and curvature of the complex-octonion curved space have an influence on the field strength and field source of the electromagnetic and gravitational fields, impacting the angular momentum, torque, and force, especially the electromagnetic force in the curved space.