Let M be a square-free integer and P be a prime such that (M,P)=1. We prove a new level aspect hybrid subconvexity bound for L(1/2,f⊗χ) where f is a primitive (either holomorphic or Maass) cusp form of level P and χ a primitive Dirichlet character modulo M satisfying P∼Mη with 0<η<3/2−3ϑ, where ϑ is the current known approximation towards the Ramanujan-Petersson conjecture. Particularly we obtain a stronger subconvexity for max{6ϑ,1/2}<η<(3−6ϑ)/2 which has not been covered by the work of Blomer-Harcos [0].