Accurate prediction of electricity prices plays an essential role in the electricity market. To reflect the uncertainty of electricity prices, price intervals are predicted. This paper proposes a novel prediction interval construction method. A conditional generative adversarial network is first presented to generate electricity price scenarios, with which the prediction intervals can be constructed. Then, different generated scenarios are stacked to obtain the probability densities, which can be applied to accurately reflect the uncertainty of electricity prices. Furthermore, a reinforced prediction mechanism based on the volatility level of weather factors is introduced to address the spikes or volatile prices. A case study is conducted to verify the effectiveness of the proposed novel prediction interval construction method. The method can also provide the probability density of each price scenario within the prediction interval and has the superiority to address the volatile prices and price spikes with a reinforced prediction mechanism.