Since rumor spreading in social network is inevitably affected by social and environmental factors, the influence of two main social effects, conformity effect and authoritative effect, on rumor spreading were discussed by combining theoretical analysis and simulation experiments. Firstly, the population in social network was divided into four types:Susceptible (S), Hesitated (H), Infected (I) and Removed (R), an SHIR rumor spreading model was established based on a new state transition rule. Secondly, the iterative technique and fitting approach were used to reveal the relations between rumor spreading and the density of initial spreaders or initial spreading rate. Finally, two kinds of social effects, conformity effect and authoritative effect, were characterized at individual level, and their influences on rumor spreading were simulated and analyzed. The experimental results show that the spreading peak values of rumor have a linear relation to the density of initial spreader, while the peak time has a sharp decline with the increasing of density of initial spreader. The more initial spreading rate, the higher the spreading peak value and the shorter peak time. The conformity effect and authoritative effect can significantly increase the range and velocity of rumor spreading, and greatly promote the proportion of the removed in steady-state network; the higher the network density, the faster and wider the rumor spreading, but conformity effect is stronger than authoritative effect at same networks, and their difference become smaller and smaller with increasing of network density; the more important the initial spreaders, the faster and wider the rumor spreading, but authoritative effect is more prominent than conformity effect.