Disclosed in the present application is a method for a terminal periodically reporting, to a base station, channel state information on the basis of a linear combination codebook in a wireless communication system. Particularly, the method comprises the steps of: receiving a reference signal from the base station; and reporting channel state information which has been outputted to the base station on the basis of the reference signal, wherein the channel state information includes a channel quality indicator and information relating to a precoding matrix index, and when a rank outputted on the basis of the reference signal is 2, the precoding matrix index is selected from a codebook which has been sub-sampled, wherein a precoding matrix constituting the sub-sampled codebook comprises a first column vector for a first layer and a second column vector for a second layer that crosses the first column vector, wherein the information relating to the precoding matrix index indicates three co-phase coefficients defining the first column vector as a 4-bit size, and wherein three co-phase coefficients defining the second column vector are identical to the three co-phase coefficients defining the first column vector.