Understanding the emergence and diffusion of extreme opinions becomes important to our globalized society. In this study, we propose a social judgment based opinion (SJBO) dynamics model, which incorporates both the compromise between similar opinions and the repulsion between discrepant opinions, to study the occurrence and spread of extremism in two different scenarios. The first concerns a situation in which individuals interact with each other through their inner opinions, while the second involves a case that each individual updates his inner opinion and choice via observing his neighbor’s choice. The simulation results show that, in the first scenario, a critical uncertainty level is present, at which the size of extremists can be maximized. Increasing or decreasing the uncertainty level from the critical value can diminish or even eliminate the extremists. In the second scenario, high uncertainty level tends to promote the development of extremists. However, the extremism can be contained or even avoided if the influence scope of silencers is large enough. In both scenarios, a large level of tolerance can help to reduce extremists as well.