A method for feeding back Channel State Information, CSI, in a multi-input multi-output system, comprising: feeding back, by a User Equipment, UE, CSI comprising codebook index information to an evolved Node B, eNodeB, wherein the codebook index information comprises: a first type of codebook index set I and a second type of codebook index set J; a combination of the first type of index set I and the second type of index set J is used for indicating a precoding matrix U, and the precoding matrix U is an N t × r matrix, where N t represents a total number of ports or a total number of antennas and r represents a number of transmission layers; the precoding matrix U is composed of at least Q × r basic vectors having a dimension of N t Q, where Q ≥2, r ≥1, and Q and r are both positive integers; the basic vectors are columns extracted from a matrix B composed of M columns of N t Q -dimensional vectors, where M is a positive integer; a union of the first type of index set I and the second type of index set J comprises codebook indication information i 1, i 2 and i 3; the codebook indication information i 1 is used for representing selection information of K matrixes W i 1 1 ···W i 1 k, where K is a positive integer, each column of the K matrixes W i 1 1 ···W i 1 k is extracted from column vectors comprised in the matrix B; i 3 is used for representing a matrix W i 1 l selected from the K matrixes; i 2 is used for representing information of one or more basic vectors extracted from the matrix W i 1 l and used to construct the precoding matrix U; wherein the precoding matrix U meets a model: U = ν 0 βν 1 or U = ν 0 ′ αν 1 ′ βν 2 ′ αβν 3 ′ or U = ν 0 ν 2 βν 1 − βν 3 or U = ν 0 ′ ν 4 ′ αν 1 ′ αν 5 ′ βν 2 ′ − βν 6 ′ αβν 3 ′ − αβν 7 ′, where, vectors v 0, v 1, v 2 and v 3 are vectors having a dimension of N t 2 × 1, vectors v 0 ′, v 1 ′, v 2 ′, v 3 ′, v 4 ′, v 5 ′, v 6 ′ and v 7 ′ are vectors having a dimension of N t 4 × 1, α = e jθ 1, and β = e jθ 2, where 0 ≤ θ 1 ≤ 2π, 0 ≤ θ 2 ≤ 2π. feeding back, by a User Equipment, UE, CSI comprising codebook index information to an evolved Node B, eNodeB, wherein the codebook index information comprises: a first type of codebook index set I and a second type of codebook index set J; a combination of the first type of index set I and the second type of index set J is used for indicating a precoding matrix U, and the precoding matrix U is an N t × r matrix, where N t represents a total number of ports or a total number of antennas and r represents a number of transmission layers; the precoding matrix U is composed of at least Q × r basic vectors having a dimension of N t Q, where Q ≥2, r ≥1, and Q and r are both positive integers; the basic vectors are columns extracted from a matrix B composed of M columns of N t Q -dimensional vectors, where M is a positive integer; a union of the first type of index set I and the second type of index set J comprises codebook indication information i 1, i 2 and i 3; the codebook indication information i 1 is used for representing selection information of K matrixes W i 1 1 ···W i 1 k, where K is a positive integer, each column of the K matrixes W i 1 1 ···W i 1 k is extracted from column vectors comprised in the matrix B; i 3 is used for representing a matrix W i 1 l selected from the K matrixes; i 2 is used for representing information of one or more basic vectors extracted from the matrix W i 1 l and used to construct the precoding matrix U; wherein the precoding matrix U meets a model: U = ν 0 βν 1 or U = ν 0 ′ αν 1 ′ βν 2 ′ αβν 3 ′ or U = ν 0 ν 2 βν 1 − βν 3 or U = ν 0 ′ ν 4 ′ αν 1 ′ αν 5 ′ βν 2 ′ − βν 6 ′ αβν 3 ′ − αβν 7 ′, where, vectors v 0, v 1, v 2 and v 3 are vectors having a dimension of N t 2 × 1, vectors v 0 ′, v 1 ′, v 2 ′, v 3 ′, v 4 ′, v 5 ′, v 6 ′ and v 7 ′ are vectors having a dimension of N t 4 × 1, α = e jθ 1, and β = e jθ 2, where 0 ≤ θ 1 ≤ 2π, 0 ≤ θ 2 ≤ 2π.