The seat unit of a stroller includes a seat frame mounted on a stroller frame, a backrest frame unit, and a pad assembly. The backrest frame unit includes a backrest support mounted on the seat frame, and a movable frame member connected pivotally to the backrest support and pivotable from a folded position, where the movable frame member is disposed proximate to the backrest support to form a seating space adapted for seating of a baby therein, to an unfolded position, where the movable frame member extends inclinedly from the backrest support to form a reclining space adapted for reclining of the baby therein. The pad assembly includes a seat pad, a back pad and a backrest pad mounted on the seat frame, the backrest support and the movable frame member, respectively.