Anew real-space numerical implementation of the self-consistent field theory for semiflexible polymers is developed. Specifically, a finite volume algorithm on a unit sphere with an icosahedron triangular mesh is employed to describe the orientation degree of freedom of the wormlike chains. The validity of the new method is analyzed by comparing with results from the spectral method. As a concrete example, the new numerical method is applied to the self-assembly of rod-coil diblock copolymers within the framework of Onsager excluded-volume interaction. A variety of liquid crystalline phases such as disordered isotropic, nematic, and smectic phases have been obtained. In particular, the new method provides a particularly convenient method for studying the smectic-C phase. A phase diagram is constructed for the rod-coil diblock copolymers, which is in agreement with previous theoretical and experimental results.