in the electrolysis of H₂SO₄ solution, when the concentration is increased why does the current increase even when OH⁻ ions reduce?
Near room temperature, considering solutions of water and sulphuric acid, the maximum conductivity is at about 30% sulfuric acid.  For pure water or pure sulfuric acid the conductivity is orders of magnitude lower.  

In pure water, there are only $10^{-7}$M of $\ce{H+}$ and $\ce{OH-}$ to carry current.  

When a relatively small amount of sulfuric acid  is added, it dissociates fully to $\ce{H+}$ and $\ce{HSO4-}$.  For example if you increase the concentration of sulfuric acid from 0M to 0.01 M, the number of ions in the solution increase by a factor of $10^5$.