So far, the theory of fuzzy integrals is much wide and complete, but all the integrands are point-valued functions. The paper's purpose is to extend the integrand to set-valued functions, and establish the fuzzy integral of set-valued functions, such that the fuzzy integral of point-valued functions is a special case. The method used here is similar to Aumann's, and the basing fuzzy integral is the generalized fuzzy integral given in. Various kinds of properties and convergence theorems are shown for the fuzzy integral of set-valued functions.