In this paper, we extend the endoscopic transfer of definite unitary group U(n), which sends a pair of automorphic forms of U(n1), U(n2) to an automorphic form of U(n1 + n2), to finite slope p-adic automorphic forms for definite unitary groups by constructing a rigid analytic map between eigenvarieties n1 × n2 → (n1+n2), which at classical points interpolates endoscopic transfer map. © 2016 Ramanujan Mathematical Society.