In spite of the observation of various exotic correlated physics in twisted graphene and transition metal dichalcogenides, it remains a great challenge to prepare twisted bilayers of puckered elemental layered crystals in the developing field of twistronics. Here, we report the first discovery and success in epitaxial growth of the 39°-twisted bilayer α-Sb. Molecular dynamics simulations verify that the 39°-twisted bilayer α-Sb is energetically stable, consistent with the experiments. Scanning tunneling spectroscopy in combination with first-principles calculations confirms that the 39°-twisted bilayer α-Sb is metallic, whereas the AB-stacked bilayer α-Sb appears semiconducting. Such a twist-dependent semiconductor-to-metal transition can be rationalized by the fact that the twist-induced reconstruction facilitates enhanced interlayer electron hopping between the p