There is little I can do to help him.

整个句子补充完整是There is little help which/that I can do to help him.因为后面有动词help,所以前面可以省略.I can do 是which或that做先行词引导的定语从句,修饰little help .先行词在句子中不作句法成分,又不引起歧义时,可以省略.to help him是介词短语做整个句子的目的状语.