J. C. Maxwell applied the quaternion analysis and the vector terminology to depict the electromagnetic theory. Nowadays the scholars can use the complex quaternion to study the electromagnetic feature, including the Maxwell’s equations and the current continuity equation etc. Meanwhile it is able to describe the gravitational theory with the complex quaternion. On the basis of these studies, the paper separates the complex octonion into two components, the complex quaternion and the complex S-quaternion. The complex quaternion is suitable to describe the gravitational theory, while the complex S-quaternion is proper to depict the electromagnetic theory. Further the paper can apply the complex quaternion to describe the wave equation of gravitational field, and use the complex S-quaternion to depict the wave equation of electromagnetic field. The result reveals that the complex octonion is suitable to describe simultaneously the wave features of electromagnetic and gravitational fields.