Motivated by a desire to find a useful 2d Lorentz-invariant reformulation of the AdS_5 x S 5 superstring world-sheet theory in terms of physical degrees of freedom we construct a Pohlmeyer-reduced version of the corresponding sigma model. Starting with a coset space string sigma model in the conformal gauge and writing the classical equations in terms of currents one can fix the residual conformal diffeomorphism symmetry and kappa-symmetry and introduce a new set of variables (related locally to currents but non-locally to the original string coordinate fields) so that the Virasoro constraints are automatically satisfied. The resulting gauge-fixed equations can be obtained from a Lagrangian of a non-abelian Toda type: a gauged WZW-model with an integrable potential coupled also to a set of 2d fermionic fields. We show that in the special case of the AdS_2 x S2 superstring model the reduced theory is equivalent to the N=2 supersymmetric extension of the sine-Gordon model.