A radial foil bearing for enclosing and supporting a rotary shaft, the radial foil bearing comprising: a cylindrical top foil disposed so as to face the rotary shaft; a back foil disposed on a radially outer side of the top foil; and a cylindrical bearing housing accommodating the top foil and the back foil, wherein the back foil is formed in a cylindrical shape using at least one back foil piece, and wherein the back foil piece includes peak portions and valley portions which are alternately formed in a circumferential direction of the top foil and is fixed to the bearing housing at an intermediate portion between both end portions in a circumferential direction of the back foil piece, characterized in that notches are formed in edges on both sides of a valley portion in the axial direction of the radial foil bearing, the valley portion being positioned at the intermediate portion of the back foil piece, engagement grooves are formed in the bearing housing, and the notches are formed at positions corresponding to the engagement grooves, the width and the depth of each notch are formed to be the same as the width and the depth of each engagement groove, respectively, a locking member is locked with the notches of the back foil piece and with the engagement grooves of the bearing housing so that the back foil piece is fixed to the bearing housing, such that both ends of the back foil piece become free ends, the locking member is formed in a U-shape which includes a pair of engagement legs, and a connection portion which connects the engagement legs together so as to be disposed at one ends of the engagement legs, and one engagement leg of the engagement legs engages with the engagement groove and the notch of one side surface of the radial foil bearing, and the other engagement leg of the engagement legs engages with the engagement groove and the notch of the other side surface of the radial foil bearing. a cylindrical top foil disposed so as to face the rotary shaft; a back foil disposed on a radially outer side of the top foil; and a cylindrical bearing housing accommodating the top foil and the back foil, wherein the back foil is formed in a cylindrical shape using at least one back foil piece, and wherein the back foil piece includes peak portions and valley portions which are alternately formed in a circumferential direction of the top foil and is fixed to the bearing housing at an intermediate portion between both end portions in a circumferential direction of the back foil piece, characterized in that notches are formed in edges on both sides of a valley portion in the axial direction of the radial foil bearing, the valley portion being positioned at the intermediate portion of the back foil piece, engagement grooves are formed in the bearing housing, and the notches are formed at positions corresponding to the engagement grooves, the width and the depth of each notch are formed to be the same as the width and the depth of each engagement groove, respectively, a locking member is locked with the notches of the back foil piece and with the engagement grooves of the bearing housing so that the back foil piece is fixed to the bearing housing, such that both ends of the back foil piece become free ends, the locking member is formed in a U-shape which includes a pair of engagement legs, and a connection portion which connects the engagement legs together so as to be disposed at one ends of the engagement legs, and one engagement leg of the engagement legs engages with the engagement groove and the notch of one side surface of the radial foil bearing, and the other engagement leg of the engagement legs engages with the engagement groove and the notch of the other side surface of the radial foil bearing.