The difference counterpart of the Brücke conjecture was investigated.By virtue of the Borel lemma and the property about periodic functions in the Nevanlinna's value distribution theory to exclude all cases which may occurr when the order of an entire function satisfying some conditions is greater than or equal to 1,and utilizing some proved conclusions about the uniqueness of entire function of finite order,it is proved that if an entire function of hyper-order,which has a small Picard exceptional function,shares the value of 0 with its difference operator,then the form of this entire function can be obtained.In addition,some results about the order in Nevanlinna's value distribution theory have been also adopted,so that Borel lemma can be applied repeatedly in the theorem proving.The method is suited to the sharing value and some cases of difference sharing periodic functions.