Abstract: The design of \emph{de novo} functional proteins that bind with specific ligand molecules is crucial in various domains like therapeutics and bio-engineering. One vital yet challenging step is to design the protein pocket, the cavity region of protein where the ligand binds with. Existing methods suffer from inefficient generation, insufficient context modeling (ligand molecule), and incapability of generating sidechain atoms. To overcome the limitations, we propose a \textbf{F}ull-\textbf{A}tom \textbf{I}terative \textbf{R}efinement framework (\textbf{FAIR}) for protein pocket sequence (i.e., residue types) and 3D structure co-design. Generally, FAIR consists of two steps that follow a coarse-to-fine pipeline (backbone atoms to full atoms including sidechain) for full-atom generation. For efficiency, all residue types and structures are updated together in each round (i.e., full-shot refinement). In the first step, the residue types and backbone coordinates are updated with a hierarchical context encoder and two structure refinement modules capturing inter-residue and pocket-ligand interactions. The second step further models the sidechain atoms of pockets and updates residue types to achieve sequence-structure consistency. The structure of the binding ligand is also updated along with the above refinement iterations accounting for its flexibility. Finally, extensive evaluations showthat FAIR outperforms baselines in efficiently designing high-quality pocket sequences and structures. Specifically, the average improvements on AAR and RMSD are over 10$\%$.