Domain adaptation is suitable for transferring knowledge learned from one domain to a different but related domain. Considering the substantially large domain discrepancies, learning a more generalized feature representation is crucial for domain adaptation. On account of this, we propose an adaptive component embedding (ACE) method, for domain adaptation. Specifically, ACE learns adaptive components across domains to embed data into a shared domain-invariant subspace, in which the first-order statistics is aligned and the geometric properties are preserved simultaneously. Furthermore, the second-order statistics of domain distributions is also aligned to further mitigate domain shifts. Then, the aligned feature representation is classified by optimizing the structural risk functional in the reproducing kernel Hilbert space (RKHS). Extensive experiments show that our method can work well on six domain adaptation benchmarks, which verifies the effectiveness of ACE.