Let q be a large prime,and x the quadratic character modulo q.Let φ be a self-dual Hecke-Maass cusp form for SL(3,Z),and uj a Hecke-Maass cusp form for Γ0(q) ∈ SL(2,Z) with spectral parameter tj.We prove,for the first time,some hybrid subconvexity bounds for the twisted L-functions on GL(3),such as L(1/2,φ × uj × x) ＜＜φ,ε (q(1 + |tj|))3/2-θ+ε and L(1/2+it,φ × x) ＜＜φ,ε (q(1 + |t|))3/4-θ/2+ε for any ε ＞ 0,where θ =1/23 is admissible.The proofs depend on the first moment of a family of L-functions in short intervals.In order to bound this moment,we first use the approximate functional equations,the Kuznetsov formula,and the Voronoi formula to transform it to a complicated summation,and then we apply different methods to estimate it,which give us strong bounds in different aspects.We also use the stationary phase method and the large sieve inequalities.