•Evolutionary game theory and complex network theory are combined to investigate epidemic spreading.•A rewarding mechanism is introduced to enhance the strategy of self-isolation.•Larger network degree is conducive to the prevalence of self-isolation, thereby hindering epidemic spreading. How to effectively control virus spreading remains an open challenging problem since the environments for virus propagation are complex and heterogeneous, and more importantly, the dynamics of virus spreading usually co-evolves with that of human beings' travelling behavior. Motivated by this, we combine evolutionary game theory and complex network theory to investigate the influence of the competition between different travelling strategies on virus propagation. Simulation results show that the strategy of self-isolation can substantially inhibit the spread of infectious diseases on complex social networks, and introducing rewarding mechanism would further enhance this effect. Moreover, counterintuitively, larger network degree is conducive to the prevalence of self-isolation, thereby hindering virus spreading. We hope our work can provide more insight into the effective control of virus propagation in the real world.