Based on S-rough sets(singular rough sets), this paper presents function S-rough sets (function singular rough sets)and its mathematical structures and features. Function S-rough sets has two forms: function one direction S-rough sets (function one direction singular rough sets) and function two direction S-rough sets (function two direction singular rough sets). This paper advances the relationship theorem of function S-rough sets and S-rough sets. Function Srrough sets is the general form of S-rough sets, and S-rough sets is the special case of function Srough sets. In this paper, applications of function S-rough sets in rough law mining-discovery of system are given. Function S-rough sets is a new research direction of rough sets and rough system.