The recent coronavirus pandemic (COVID-19) has negatively impacted the whole economy, especially the oil industry, in at least two ways. First, it created a demand shock as COVID-19 reduced global demand for crude oil, increased uncertainty, and triggered a serious economic recession in most developed and emerging countries. Second, it led to a supply shock as the pandemic resulted in an oil trade war between the major oil-producing nations (Saudi Arabia and Russia). Both shocks led to very high levels of oil price volatility. Our paper explores the dynamics of this volatility and explains the effects of these two shocks (induced by an adjustment of oil demand and supply) on West Texas Intermediate (WTI) crude oil price volatility. Accordingly, we show that oil price volatility reacted substantially to the pandemic-induced oil shocks. In particular, we document the impact of uncertainty caused by these shocks and investor anxiety on oil price volatility. We show that greater uncertainty leads to more oil price volatility. Our findings remained unchanged even after controlling for modeling robustness.