The invention provides a preparation method for a sulfur-free or ultralow-sulfur-content Y molecular sieve. A conventional preparation scheme for a NaY molecular sieve is employed; and raw materials consisting of soluble glass, sodium metaaluminate, a NaOH solution and deionized water are mixed to form glue and then a hydrothermal reaction is carried out so as to prepare the sulfur-free or ultralow-sulfur-content Y molecular sieve. The preparation method is characterized in that a certain amount of soluble barium salt is added before usage of the raw materials, full stirring and standing are successively carried out, and then supernatant liquid is taken as a raw material for preparation of the Y molecular sieve; and a certain amount of soluble barium salt is added into solutions used in subsequent exchanging and washing, and only supernatant liquid is taken for usage.