Electronic band structure and electronic density of states (DOS) of single‐walled helically coiled carbon nanotubes (HCCNTs) are numerically calculated by symmetry implemented density functional tight binding method. It is found that unlike straight single‐walled carbon nanotubes, single‐walled HCCNTs can be semi‐metallic, having high DOS at Fermi level. We show that this is a consequence of the local structure of HCCNTs, i.e., that by changing positions of pentagons and heptagons within a monomer, transitions between metallic, semi‐metallic, quasi‐metallic, and semiconducting structures can be made.