The aerosol effects on clouds and precipitation in deep convective cloud systems are investigated using the Weather Research and Forecast (WRF) model with the Morrison two-moment bulk microphysics scheme. Considering positive or negative relationships between the cloud droplet number concentration (N(c)) and spectral dispersion (epsilon), a suite of sensitivity experiments are performed using an initial sounding data of the deep convective cloud system on 31 March 2005 in Beijing under either a maritime ('clean') or continental ('polluted') background. Numerical experiments in this study indicate that the sign of the surface precipitation response induced by aerosols is dependent on the epsilon-N(c) relationships, which can influence the autoconversion processes from cloud droplets to rain drops. When the spectral dispersion epsilon is an increasing function of N(c), the domain-average cumulative precipitation increases with aerosol concentrations from maritime to continental background. That may be because the existence of large-sized rain drops can increase precipitation at high aerosol concentration. However, the surface precipitation is reduced with increasing concentrations of aerosol particles when epsilon is a decreasing function of N(c). For the epsilon-N(c) negative relationships, smaller spectral dispersion suppresses the autoconversion processes, reduces the rain water content and eventually decreases the surface precipitation under polluted conditions. Although differences in the surface precipitation between polluted and clean backgrounds are small for all the epsilon-N(c) relationships, additional simulations show that our findings are robust to small perturbations in the initial thermal conditions.