In this paper, we delve into the critical role of oil shocks in influencing the systematic risk of G7 stock markets—a concern of paramount importance given the interconnectedness of global economies and the pivotal role of energy markets. We employ Delta Conditional Value at Risk (ΔCoVaR) and Marginal Expected Shortfall (MES) to measure the systematic risk of G7 stock markets due to volatility in the oil market. By decomposing oil price change into oil supply shocks, aggregate demand shocks, and oil-specific demand shocks using a structural vector autoregression model, we offer a more granular perspective to investigate the time-varying effects of oil price fluctuations on the systematic risk of G7 stock markets. The results indicate that the impact of oil supply shock is insignificant compared with aggregate demand shock and speculative demand shock. Speculative demand shock contributes the most to systematic risk in the short term, but their impact declines as the number of periods increases. In the long term, the biggest impact on systematic risk is aggregate demand shock. Additionally, we construct a network among G7 stock markets and oil structural shocks based on time-varying spillover and the empirical results show that G7 stock markets play a role as receiver and all oil structural shocks as emitter. Besides, Japan is the country in G7 countries most affected by oil shocks.