Opinion competition is a common phenomenon in real life, such as opinions on controversial issues or political candidates, however modeling the competition remains largely unexplored. To bridge this gap, we propose a model of competing opinion diffusion on social networks taking into account the degree-dependent fitness or persuasiveness.We study the combined influence of social networks, individual fitnesses and attributes, as well as mass media on people’s opinions, and find that both social networks and mass media act as amplifier in opinion diffusion for which the amplifying effect can be quantitatively characterized. We analytically obtain the probability that each opinion will ultimately pervade the whole society when there are no committed people in networks, and the final proportion of each opinion at the steady state when there are committed people in networks. The results of numerical simulations show good agreement with those obtained through analytical approach. This study provides insight into the collective influence of individual attributes, local social networks and global media on opinion diffusion, and contributes to a comprehensive understanding of competing diffusion behaviors in real world.