The equation of rotating surface is one of the key contents in the teaching of vector algebra and spatial analytic geometry in higher mathematics. The existing higher mathematics textbooks mostly concern the solution methods of the surface equation formed by the rotation of the coplanar curve on the coordinate plane around the coordinate axis. Based on the equation of the such rotating surfaces, this paper deduces the equation of the general rotating surface formed by rotating a space curve around a fixed space line by using the formula of direction angle and rotation axis. It determines the rotation axis by looking for attitude and its relative position between the two coordinate systems. The method for solving the general equation of rotating surface proposed in this paper not only is a useful supplement to the current teaching content, but also provides a practical reference for constructing the surface rotation.