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