Being able to predict people's opinions on issues and behaviors in realistic scenarios can be helpful in various domains, such as politics and marketing. However, conducting large-scale surveys like the European Social Survey to solicit people's opinions on individual issues can incur prohibitive costs. Leveraging prior research showing influence of core human values on individual decisions and actions, we propose to use value-injected large language models (LLM) to predict opinions and behaviors. To this end, we present Value Injection Method (VIM), a collection of two methods -- argument generation and question answering -- designed to inject targeted value distributions into LLMs via fine-tuning. We then conduct a series of experiments on four tasks to test the effectiveness of VIM and the possibility of using value-injected LLMs to predict opinions and behaviors of people. We find that LLMs value-injected with variations of VIM substantially outperform the baselines. Also, the results suggest that opinions and behaviors can be better predicted using value-injected LLMs than the baseline approaches.