Let Fq[t] be the ring of polynomials over the finite field Fq. In this talk, we will discuss a generalization of Vinogradov’s mean value theorem in Fq[t]. We will apply our result to obtain an upper bound for G˜ q(k), which is the least integer s such that every polynomial in Fq[t] of sufficiently large degree, the expected asymptotic formula in Waring’s problem holds. This is a joint work with Trevor Wooley.