This paper is aimed at a combined theoretical and numerical study of the force-extension relation of a short DNA molecule stretched in an electrolyte. A theoretical formula based on a recent discrete wormlike chain (WLC) model of Kierfeld et al. (Eur Phys. J. E, Vol. 14, pp.17-34, 2004) and the classical OSF mean-field theory on electrostatic stiffening of a charged polymer is numerically verified by a set of Brownian dynamics simulations based on a generalized bead-rod (GBR) model incorporating long-ranged electrostatic interactions via the Debye-Hueckel potential (DH). The analysis indicates that the stretching of a short DNA can be well described as a WLC with a constant effective persistent length. This contrasts the behavior of long DNA chains that are known to exhibit variable persistent lengths depending on the ion concentration levels and force magnitudes.