  A perturbative calculation of the three-nucleon ground-state energy shift in
a finite volume is carried out within the non-relativistic effective theory.
The energy shift is evaluated up to and including $\mathcal{O}(L^{-6})$, where
$L$ is the size of a cubic box. The convergence of the perturbative series at
physical values of the scattering lengths is studied numerically.
