  In this paper, we extend the surface growth scheme in AdS spacetime with a
boundary in the AdS/BCFT correspondence. We show that the entanglement wedge
with a boundary can be constructed from the direct growth of bulk extremal
surfaces layer by layer. In addition, we find that the surface growth
configuration in BCFT can be connected with the defect multi scale entanglement
renormalization ansatz (MERA) tensor network. Furthermore, we also investigate
the entanglement of purification within the surface growth process, which
reveals more refined structure of entanglement entropy and indicates a
selection rule for surface growth in the bulk reconstruction.
