We report six phases of high-density nano-ice predicted to form within carbon nanotubes (CNTs) at high pressure. High-density nano-ice self-assembled within smaller-diameter CNT (17,0) exhibits a double-walled helical structure where the outer wall consists of four double-stranded helixes, which resemble a DNA double helix, and the inner wall is a quadruple-stranded helix. Four other double-walled nano-ices, self-assembled respectively in two larger-diameter CNTs (20,0 and 22,0), display tubular structure. Within CNT (24,0), the confined water can freeze spontaneously into a triple-walled helical nano-ice where the outer wall is an 18-stranded helix and the middle and inner walls are hextuple-stranded helixes.