LetΠ (resp. Σ) bea cohomological (for the trivial coefficient) cuspidal automorphic representation of GL(3) (resp. GL(2)) over a CM number field, and assume that they are base change from unitary groups.We prove the following theorem: if the Rankin-Selberg L-functionL(Π×Σ, s) does not vanish at its center, then the associatedℓ-adic Bloch-Kato Selmer group vanishes (for primesℓwherethe modℓGalois representations satisfy certain mild conditions). Theconditions onℓcome from Euler system type argument. We will discuss some examples from elliptic curves. This is a joint work with Yifeng Liu, Yichao Tian, Liang Xiao, and Xinwen Zhu.