Abstract: An intuitive portrayal of the correlation between the carbon and energy markets is essential for risk control and green financial investment management. In this paper, we investigate the asymmetric spillovers between the carbon market and energy market returns. To achieve that, we improve the Diebold–Yilmaz index model by a time-varying vector autoregressive (TVP-VAR) model. In a unified network, our daily dataset includes the closing prices of the Hubei carbon market, Shenzhen carbon market, coal futures, and energy stock index. The findings reveal that both the Hubei and Shenzhen pilots typically generate net information spillovers on energy futures. In connection with energy stocks, the Hubei carbon market acts as a net receiver, while the Shenzhen carbon market is a net transmitter. Compared with the Hubei pilot, the Shenzhen pilot is more tightly connected to the energy markets. Furthermore, the spillovers of the carbon markets exhibit significant asymmetry. In most cases, they have more substantial impacts on the energy markets when the prices of emission allowances rise. The direction and magnitude of asymmetric spillovers across markets vary over time and can be influenced by certain economic or political events.