A paper sheet conveying apparatus includes: a conveying path in which a paper sheet is conveyed; a plurality of conveying rollers; a plurality of driving motors; an out-of-step detection portion; a stop control portion; and a driving restart control portion. The plurality of conveying rollers are disposed along the conveying path. The plurality of driving motors rotates the conveying rollers. The out-of-step detection portion detects an out-of-step in each of the driving motors. The stop control portion stops each of the driving motors when an out-of-step is detected. The driving restart control portion drives, after each of the driving motors is stopped, a first driving motor in which an out-of-step has occurred, and a second driving motor in which no out-of-step occurs, under a driving start condition that an amount of rotation of the second driving motor is less than an amount of rotation of the first driving motor.