A refrigerator comprising: a cabinet having at least one storage chamber; LED lamps installed at a side wall within the cabinet; upper and lower hinges mounted at the cabinet; an inner door coupled to the upper and lower hinges to selectively open or close the storage chamber, the inner door having front and rear surfaces open to have a shape of rectangular frame; a basket installation unit mounted onto an inner surface of the inner door; an outer door disposed at a front of the inner door to selectively open or close an inner space of the inner door; an inner door cover able to selectively open or close the inner space of the inner door based on a vertical rotational shaft installed at the basket installation unit; at least one part of the basket installation unit or the inner door cover being made of a transparent material; and wherein the basket installation unit is positioned adjacent to the LED lamps when the inner door closes the storage chamber, wherein the inner door cover comprises: a support portion and cover portions (164, 166) installed at upper and lower sides of the support portion, respectively, wherein a latch is installed at the support portion, wherein the basket installation unit is partitioned into two spaces by a barrier and a latch fixing member is mounted to one side of the barrier to be engaged with the latch, and wherein a buffer is installed at one corner of the inner door so as to buffer an impact caused during opening or closing of the inner door cover. a cabinet having at least one storage chamber; LED lamps installed at a side wall within the cabinet; upper and lower hinges mounted at the cabinet; an inner door coupled to the upper and lower hinges to selectively open or close the storage chamber, the inner door having front and rear surfaces open to have a shape of rectangular frame; a basket installation unit mounted onto an inner surface of the inner door; an outer door disposed at a front of the inner door to selectively open or close an inner space of the inner door; an inner door cover able to selectively open or close the inner space of the inner door based on a vertical rotational shaft installed at the basket installation unit; at least one part of the basket installation unit or the inner door cover being made of a transparent material; and wherein the basket installation unit is positioned adjacent to the LED lamps when the inner door closes the storage chamber, wherein the inner door cover comprises: a support portion and cover portions (164, 166) installed at upper and lower sides of the support portion, respectively, wherein a latch is installed at the support portion, wherein the basket installation unit is partitioned into two spaces by a barrier and a latch fixing member is mounted to one side of the barrier to be engaged with the latch, and wherein a buffer is installed at one corner of the inner door so as to buffer an impact caused during opening or closing of the inner door cover. a support portion and cover portions (164, 166) installed at upper and lower sides of the support portion, respectively, wherein a latch is installed at the support portion, wherein the basket installation unit is partitioned into two spaces by a barrier and a latch fixing member is mounted to one side of the barrier to be engaged with the latch, and wherein a buffer is installed at one corner of the inner door so as to buffer an impact caused during opening or closing of the inner door cover.