Let p > 1 and let q denote the number such that ( 1 / p ) + ( 1 / q ) = 1 . We give a necessary condition for the product of Toeplitz operators T f T g ¯ to be bounded on the weighted Bergman space of the unit ball A α p ( α > − 1 ), where f ∈ A α p and g ∈ A α q , as well as a sufficient condition for T f T g ¯ to be bounded on A α p . We use techniques different from those in [K. Stroethoff, D. Zheng, Bounded Toeplitz products on Bergman spaces of the unit ball, J. Math. Anal. Appl. 325 (2007) 114–129], in which the case p = 2 was proved.