We evaluate the $\Lambda$-parameter in the $\overline{\mathrm{MS } }$ scheme<br />
for the pure SU(3) gauge theory with the twisted gradient flow (TGF) method. A<br />
running coupling constant $g_{\mathrm{TGF } }^2(1/L)$ is defined in a finite<br />
volume box with size of $L^4$ with the twisted boundary condition. This defines<br />
the TGF scheme. Using the step scaling method for the TGF coupling with lattice<br />
simulations, we can evaluate the $\Lambda$-parameter non-perturbatively in the<br />
TGF scheme. In this paper we determine the dimensionless ratios,<br />
$\Lambda_{\mathrm{TGF } }/\sqrt{\sigma}$ and $r_{0}\Lambda_{\mathrm{TGF } }$<br />
together with the $\Lambda$-parameter ratio<br />
$\Lambda_{\mathrm{SF } }/\Lambda_{\mathrm{TGF } }$ on the lattices numerically.<br />
Combined with the known ratio<br />
$\Lambda_{\overline{\mathrm{MS } }}/\Lambda_{\mathrm{SF } }$, we obtain<br />
$\Lambda_{\overline{\mathrm{MS } }}/\sqrt{\sigma} = 0.517(10)(^{+8}_{-7})$ and<br />
$r_{0}\Lambda_{\overline{\mathrm{MS } }}=0.593(12)(^{+12}_{-9})$, where the first<br />
error is statistical one and the second is our estimate of systematic<br />
uncertainty.