The invention discloses an over-water movable vehicle and a rudder thereof. The rudder of the over-water movable vehicle comprises a fixed rudder plate, an expansion piece and a first elastic component, wherein the expansion piece is pivoted with the fixed rudder plate; the first elastic component is connected with the fixed rudder plate and the expansion piece and supports the expansion piece; and the expansion piece presses the first elastic component under stress so that the expansion piece can rotate relative to the fixed rudder plate. In the invention, by the rotation of the expansion piece relative to the fixed rudder plate, when the rudder of a surfboard collides with a surfer or other people who is engaged in over-water activities, the collision force can be lightened so as to protect the surfer or the other people who is engaged in the over-water activities from being injured.