Sung et al. [13] obtained a WLLN (weak law of large numbers) for the array ${X_{{ni},;u_n{leq}i{leq}v_n,;n{leq}1}$ of random variables under a Cesaro type condition, where ${u_n{geq}-{infty},;n{geq}1}$ and ${v_n{leq}+{infty},;n{geq}1}$ large two sequences of integers. In this paper, we extend the result of Sung et al. [13] to a martingale type p Banach space