We define and study the fuzzy Jacobson radical of a ${kappa}$-semiring. Also it is shown that the Jacobson radical of the quotient semiring R/FJR(R) of a ${kappa}$-semiring by the fuzzy Jacobson radical FJR(R) is semisimple. And the algebraic properties of the fuzzy ideals FJR(R) and FJR(S) under a homomorphism from R onto S are also discussed.