We develop a spin diffusion theory based on the exchange mechanism among polarons to understand the organic pure spin current. It is demonstrated that the exchange coupling is strong enough to induce spin transport within the organic layer with impurity concentrations higher than 1018 cm-3. By calculating the inverse spin Hall voltage in an organic spin device, we predict that the voltage depends nonmonotonically on the impurity concentration of the organic material. By tuning the doping concentration, one can achieve a maximum inverse spin Hall voltage. Our results not only explain some recent experimental data but also inspire further experimental investigation on pure spin current in organic devices with variable impurity doping.