This paper decomposes daily crude oil shocks into demand shock, supply shock and risk shock. Then, it employs Diebold and Yilmaz connectedness index approach to explore the differences for the time-varying effect of different types of structural shocks on new energy stock markets in China, Europe and the United States during the period 10 June 2009–30 October 2018. The new findings show that: 1) There are time-varying features of structural shocks to all new energy markets. 2) The crude oil demand shock and risk shock have a large explanatory ability on the returns of all new energy stock markets, while the crude oil supply shock has a small impact. 3) The influences of crude oil demand shocks on the market returns of new energy in China, Europe and the United States are 1.31%, 8.64%, and 4.47%, respectively; however, the affection of crude oil risk shocks to the market returns of new energy in the same markets are 3.17%, 7.91%, and 21.51%, respectively. 4) The crude oil demand shock and supply shock have little impact on any new energy market volatilities, but the effects of crude oil risk shocks to China and the United States’ new energy market volatilities are 2.44% and 3.14%, respectively.