A light-driven molecular rotary motor of 9-(5-methyl-2-phenyl-2-cyclopenten-1-ylidene)-9H-fluorene (MPCPF) has been designed by means of ab initio complete active space self-consistent field and its second order multireference Moller-Plesset perturbation methods. In the present model molecule of MPCPF, 9H-fluorene (as a stator) and 5-methyl-2-phenyl-2-cyclopenten-1-ylidene (as a rotor) are directly linked with each other by a C=C double bond. Even by a substitution of phenyl group, MPCPF comes to have a stable P-helical MPCPF and a metastable M-helical MPCPF, and exhibits unidirectionality around the C=C double bond. In addition, interchange of the helicity can proceed with a low energy barrier through a floppy phenyl torsional motion. This is in contrast to previous light-driven molecular rotary motors where the unidirectionality is ensured by rigid and sterically overcrowded rotors. In the full rotary process of MPCPF, therefore, constancy of the rotation speed is expected to be much more improved as well as unidirectionality.