A paper sheet conveying apparatus comprising: a driving roller configured to rotate about a driving roller shaft in response to a rotational force transmitted from a driving source; and a follower roller configured to have a fixed position in a width direction of a conveying path where a paper sheet is conveyed, and rotate about a follower roller shaft in response to rotation of the driving roller while holding the paper sheet sandwiched between the follower roller and the driving roller so as to convey the paper sheet with the driving roller from upstream to downstream on the conveying path, wherein when conveying the paper sheet from upstream to downstream on the conveying path, the driving roller moves in the width direction of the conveying path while holding the paper sheet sandwiched between the follower roller and the driving roller so as to move the paper sheet to a center in the width direction on the conveying path wherein the driving roller moves within a predetermined range in the width direction of the conveying path, the predetermined range within which a face of the driving roller is positioned opposite a face of the follower roller, characterised in that before holding the paper sheet sandwiched between the follower roller and the driving roller and concurrently moving in the width direction of the conveying path, the driving roller moves to a limit position of the predetermined range closer to where the paper sheet conveyed on the conveying path is positioned out of the center in the width direction of the conveying path, and when moving the paper sheet to the center in the width direction on the conveying path, the driving roller moves from the limit position as a starting point to move within the predetermined range, wherein the paper sheet conveying apparatus further comprises a control unit configured to determine at which position in the width direction of the conveying path the paper sheet is being conveyed based on a distinguishing result on the paper sheet by a distinguishing unit, and based on the position determined, the control unit is configured to make the driving roller move to the limit position closer to where the paper sheet is conveyed out of the center in the width direction of the conveying path. a driving roller configured to rotate about a driving roller shaft in response to a rotational force transmitted from a driving source; and a follower roller configured to have a fixed position in a width direction of a conveying path where a paper sheet is conveyed, and rotate about a follower roller shaft in response to rotation of the driving roller while holding the paper sheet sandwiched between the follower roller and the driving roller so as to convey the paper sheet with the driving roller from upstream to downstream on the conveying path, wherein when conveying the paper sheet from upstream to downstream on the conveying path, the driving roller moves in the width direction of the conveying path while holding the paper sheet sandwiched between the follower roller and the driving roller so as to move the paper sheet to a center in the width direction on the conveying path wherein the driving roller moves within a predetermined range in the width direction of the conveying path, the predetermined range within which a face of the driving roller is positioned opposite a face of the follower roller, characterised in that before holding the paper sheet sandwiched between the follower roller and the driving roller and concurrently moving in the width direction of the conveying path, the driving roller moves to a limit position of the predetermined range closer to where the paper sheet conveyed on the conveying path is positioned out of the center in the width direction of the conveying path, and when moving the paper sheet to the center in the width direction on the conveying path, the driving roller moves from the limit position as a starting point to move within the predetermined range, wherein the paper sheet conveying apparatus further comprises a control unit configured to determine at which position in the width direction of the conveying path the paper sheet is being conveyed based on a distinguishing result on the paper sheet by a distinguishing unit, and based on the position determined, the control unit is configured to make the driving roller move to the limit position closer to where the paper sheet is conveyed out of the center in the width direction of the conveying path.