This paper considers the gossiping problem in mesh-bus computers, in which n2 nodes arranged on an n×n array are connected by n column-buses and n row-buses. The algorithm we propose in this paper completes the gossiping in [n/2]+[2 n]+1 steps. Since a lower bound on the number of steps for this problem is shown to be [n/2]+[2 n]−1, it takes at most only 2 more steps than an optimal algorithm.