A swing assembly includes a support frame unit with two side legs and a horizontal bar interconnecting the side legs, a seat unit, and linking units for suspending the seat unit. The seat unit includes a rectangular base frame connected to lower ends of the linking unit. The base frame includes a pair of lateral frame sections, and front and rear rods interconnecting the lateral frame sections. A seat frame has a front end portion resting on the front rod, and a rear end portion connected pivotally to a front end portion of a backrest frame, which is pivoted to the lateral frame sections of the base frame so as to be pivotable relative to the seat frame and the base frame for moving between a flat position, in which a rear end portion of the backrest frame rests on the rear rod, and an inclined position, in which the rear end portion of the backrest frame is raised to be disposed above the rear rod. A backrest support has an upper end pivoted to an intermediate portion of the backrest frame. A retaining unit is mounted on the rear rod for releasably retaining a lower end of the backrest support so as to retain releasably the backrest frame at the inclined position.