The present invention relates to a wireless access system supporting machine type communication (MTC) and, particularly, to: a method by which an MTC terminal receives a channel state information index and feeds back channel state information on the basis of the channel state information index; and devices for supporting the method. As one aspect of the present invention, the method by which an MTC terminal feeds back channel state information (CSI) in a wireless access system for supporting machine type communication (MTC) can comprise the steps of: receiving an upper layer signal including a CQI index selected from a mother channel quality information (CQI) table; receiving a physical downlink shared channel (PDSCH) repeatedly transmitted on the basis of a modulation scheme and coding rate indicated by the CQI index; measuring CSI for the PDSCH; and feeding back the measured CSI, wherein the mother CQI table is set to include up to a signal to interference plus noise ratio (SINR) area for a maximum coverage enhancement (CE) level supported in a network, and the CQI index can be selected in consideration of a CE level supportable by the MTC terminal.