Several strands of research have aimed to bridge the gap between artificial intelligence (AI) and human decision-makers in AI-assisted decision-making, where humans are the consumers of AI model predictions and the ultimate decision-makers in high-stakes applications. However, people’s perception and understanding is often distorted by their cognitive biases, like confirmation bias, anchoring bias, availability bias, to name a few. In this work, we use knowledge from the field of cognitive science to account for cognitive biases in the human-AI collaborative decision-making system and mitigate their negative effects. To this end, we mathematically model cognitive biases and provide a general framework through which researchers and practitioners can understand the interplay between cognitive biases and human-AI accuracy. We then focus on anchoring bias, a bias commonly witnessed in human-AI partnerships. We devise a cognitive science-driven, time-based approach to de-anchoring. A user experiment shows the effectiveness of this approach in human-AI collaborative decision-making. Using the results from this first experiment, we design a time allocation strategy for a resource constrained setting so as to achieve optimal human-AI collaboration under some assumptions. A second user study shows that our time allocation strategy can effectively de-bias the human when the AI model has low confidence and is incorrect.