The present invention relates to a wireless access system, more particularly, to methods for transceiving channel state information (CSI) for supporting 256 quadrature amplitude modulation (QAM) scheme and apparatuses for supporting the methods. A method by which a terminal capable of supporting 256 QAM in a wireless access system reports CSI, according to one embodiment of the present invention, comprises the steps of: receiving a higher-layer signal for configuring a first rank indicator (RI) reference process in the terminal; measuring a channel quality for one or more CSI processes associated with the first RI reference process configured in the terminal; selecting a channel quality indication (CQI) index by using only a first CQI table or a second CQI table for the one or more CSI processes; and reporting the CSI including the CQI index. Here, the first CQI table can support up to 64 QAM and the second CQI table can support up to 256 QAM, and only the same CQI table can be applied to the one or more CSI processes associated with the first RI reference process.