Biomolecular motor system microtubule (MT)-kinesin is considered a building block for developing artificial microdevices. Recently, an active self-organization method has been established to integrate MT filaments into ring-shaped assembly that can produce rotational motion both in the clockwise and in the counterclockwise directions. In this work, we have investigated the effect of parameters such as MT and kinesin concentration, length, and rigidity of MT and type of kinesin (structure of tail region) on the preferential rotation of the ring-shaped MT assembly produced in an active self-organization. We elucidated that these factors can significantly affect the bias of rotation of the ring-shaped MT assembly, which seems to be related to the fluctuation of leading tip of moving MT filaments. This new finding might be important for designing handedness regulated artificial biomachine using the ring-shaped MT assembly in future.