We calculate Aslamazov-Larkin paraconductity σAL(T ) for a model of strongly disordered superconductors (dimensions d = 2, 3) with a large pseudogap whose magnitude strongly exceeds transition temperature Tc. We show that, within Gaussian approximation over Cooper-pair fluctuations, paraconductivity is just twice larger that the classical AL result at the same = (T − Tc)/Tc. Upon decreasing , Gaussian approximation is violated due to local fluctuations of pairing fields that become relevant at ≤ 1 1. Characteristic scale 1 is much larger than the width 2 of the thermodynamical critical region, that is determined via the Ginzburg criterion, 2 ≈ d 1 . We argue that in the intermediate region 2 ≤ ≤ 1 paraconductivity follows the same AL power law, albeit with another (yet unknown) numerical prefactor. At further decrease of the temperature, all kinds of fluctuational corrections become strong at ≤ 2; in particular, conductivity occurs to be strongly inhomogeneous in real space.