Disclosed are a motor and a recording disc drive apparatus that can prevent a fluid in a fluid dynamic bearing from being discharged to the outside. A motor according to an aspect of the invention may include: a shaft; a sleeve having a cylindrical shape and supporting the shaft such that the shaft is rotatable therein; a rotor case engaged with an upper end of the shaft and having a rotor main wall having a cylindrical shape and protruding from one surface thereof in order to receive part of the sleeve; and a cover engaged with an end portion of the rotor main wall and extending the rotor main wall, wherein at least two sealing portions preventing leaks of a fluid used to lubricate the sleeve are formed between an internal circumferential surface, defined by the rotor main wall and the cover, and an outer circumferential surface of the sleeve.