An element r of a commutative semiring R with identity is said to be identity-summand if there exists $1{ eq}a{in}R$ such that r+a = 1. In this paper, we introduce and investigate the identity-summand graph of R, denoted by ${Gamma}(R)$. It is the (undirected) graph whose vertices are the non-identity identity-summands of R with two distinct vertices joint by an edge when the sum of the vertices is 1. The basic properties and possible structures of the graph ${Gamma}(R)$ are studied.