In this paper, we give an extension of Kronecker Lemma in Banach spaced B, and there by discuss the Lp convergence of the martingale transform Ｙ＝((?)Vk(Xk-Xk-1)Ｆｎ）ｎ≥１,here X= (Xｎ,Fｎ)ｎ≥0, is a B- valued L′ limit martingale and V = (Vｎ,Fｎ)ｎ≥１ is a real-valued predictable sequence.
