  A double-stranded DNA (dsDNA) is modeled by two coupled one-dimensional
Kitaev's chain and the topological superconductivity is studied. It is shown
that the zero energy mode exists under some specific conditions. The wave
function of zero mode is calculated and it is shown that the Majorana
quasi-particles exist on the ends of each strand. By calculating the winding
number, we show that the topological phase transition can happen if the hopping
integral between two strands is very smaller than the pairing potential between
the Cooper pairs. It means that the dsDNA behaves as a trivial superconductor,
commonly, but single-stranded DNA (or two coupled ssDNA with very small hopping
between them) may behave as a non-trivial superconductor. Finally, we suggest
an experimental setup for probable detection of Majorana quasi-particle in DNA.
