A magnetic disk storage device capable of avoiding the occurrence of vibration of magnetic disks and off-track of magnetic heads with respect to the magnetic disks, including an inner shroud enclosing a disk assembly composed of a multiplicity of magnetic disks stacked in superposed relation with spacers being interposed therebetween and formed at its outer peripheral wall with first ports for inserting access arms therethrough and at its top above a spindle supporting the disk assembly with a second port, a cylindrical filter for removing dust from air flowing through the second port of the inner shroud into the interior thereof, and a dust cover enclosing the inner shroud, actuators and filter. The provision of the inner shroud is conductive to prevention of development of turbulent air flow in the vicinity of the magnetic disks. The inner shroud is further formed at its outer peripheral wall with a multiplicity of small apertures for releasing heat generated in the inner shroud to outside, to thereby avoid thermal off-track of the magnetic heads.