The observation of redshifted 21-cm absorption signal enables us to constrain the intergalactic medium (IGM) gas thermal history. According to the standard scenario of the cosmological structure formation, the sky-averaged (global) 21-cm line signal is expected to be detected as an absorption signal during the Dark Ages. In this paper, we study a possible constraint on the primordial magnetic fields (PMFs) strength with global 21-cm line observation. PMFs can heat up the IGM gas in the Dark Ages due to magnetohydrodynamic energy dissipation mechanisms. The global 21-cm absorption signal can be detected only when the IGM gas is cooler than the cosmic microwave background (CMB) photons. We solve the evolution equations for the IGM gas temperature, ionization fraction and the magnetic field strength, and investigate the global 21-cm signal with the PMFs. Moreover, we demonstrate that, if the redshift of the 21-cm absorption signal is detected at $z \simeq 17$, the PMF strength smoothed on 1 Mpc can be constrained as $B_{1\mathrm{Mpc}} \lesssim 10^{-10}$ Gauss.