讨论了B值独立同分布随机变元的矩完全收敛性，在一定矩条件下得到了B值同分布随机变元的矩完全收敛性。将相关的B值独立同分布随机变元的完全收敛的结果推广到了B值独立同分布随机变元的矩完全收敛性，得到了在矩存在的条件下与独立同分布完全收敛性相似的结果。关 键 词 完全收敛性; 独立随机变元; 随机变元和; 矩完全收敛性; 矩不等式Abstract In the paper, the moment complete convergence for sums of i.i.d. random elements in Banach Space has been discussed under certain moment condition, generalize the result of complete convergence for sums of i.i.d. random elements in Banach Space to the moment complete convergence for sums of i.i.d. random elements in Banach Space, and obtain the similar result as that of complete convergence under the certain moment condition.Key words complete convergence; i.i.d random elements; sums of random elements; moment complete convergence; inequality for moment