  In 2006 Quesne and Tkachuk (J. Phys. A: Math. Gen. {\bf 39}, 10909, 2006)
introduced a (D+1)-dimensional $(\beta,\beta')$-two-parameter Lorentz-covariant
deformed algebra which leads to a nonzero minimal length. In this work, the
Lagrangian formulation of the spinor field in a (3+1)-dimensional space-time
described by Quesne-Tkachuk Lorentz-covariant deformed algebra is studied in
the case where $\beta'=2\beta$ up to first order over deformation parameter
$\beta$. It is shown that the modified Dirac equation which contains higher
order derivative of the wave function describes two massive particles with
different masses. We show that physically acceptable mass states can only exist
for $\beta<\frac{1}{8m^{2}c^{2}}$. Applying the condition
$\beta<\frac{1}{8m^{2}c^{2}}$ to an electron, the upper bound for the isotropic
minimal length becomes about $3 \times 10^{-13}m$. This value is near to the
reduced Compton wavelength of the electron $(\lambda_c = \frac{\hbar}{m_{e}c} =
3.86\times 10^{-13} m)$ and is not incompatible with the results obtained for
the minimal length in previous investigations.
