The balance of hash functions is a newly conception introduced by Bellare .It is a measure of the "amount of regularity" of a hash function. The complexity of birthday attack on hash functions is greatly affected by the balance of it, which will decrease quickly with the reduction of the balance. Therefore the balance of hash functions can be used as a new measure of hash functions security .In this paper we study the relation between the balance of compression functions and the balance of hash functions in MD construction. A new conception, partial balance of function, is introduced and used to analyse the relation above. It can be shown that the hash function will have a good balance on the condition that the compression function has a good partial balance.