A balanced rank distribution labeling of a graph G of order n is a new kind of vertex labeling from {1, 2, 3, ..., k}(n = 6, complete graphs K-n for n >= 3 and complete bipartite graphs K-n/2,K-n/2 for even n >= 4 have been investigated and obtained the results on balanced rank distribution number (brd(G)) for the given graphs as follows: (i) brd(L-n/2) = 3n - 15, for even n >= 12 (ii) brd(K-n ) = n, for n >= 3 (iii) brd(K-n/2,K-n/2) = n, for even n >= 4