Superdeformed (SD) states in $^{40}\mathrm{Ar}$ have been studied using the deformed-basis antisymmetrized molecular dynamics. Low-energy states were calculated by the parity and angular momentum projection and the generator coordinate method (GCM). Basis wave functions were obtained by the energy variation with a constraint on the quadrupole deformation parameter $\ensuremath{\beta}$, while other quantities such as triaxiality $\ensuremath{\gamma}$ were optimized by the energy variation. By the GCM calculation, an SD band was obtained just above the ground-state band. The SD band involves a ${K}^{\ensuremath{\pi}}={2}^{+}$ side band due to the triaxiality. The calculated electric quadrupole transition strengths of the SD band reproduce the experimental values appropriately. Triaxiality is significant for understanding low-lying states.