The current electricity market trading mechanism mainly includes the bilateral negotiation transaction and centralized transaction, with defects such as information asymmetry, insufficient competition, and weak price discovery. Thus, a new double-market parallel trading mechanism is proposed to improve the efficiency of the competitive electricity market in this paper. Regard the electricity market as a price-searching market and divide into two sub-markets composed of a price-searching market for buyers and a price-searching market for sellers. Market entities can trade synchronously in two sub-markets as price searchers or bidders. Searchers are responsible for organizing transactions in line with the market clearing rule library, and bidders participate in transactions initiated by searchers. Under the parallel mechanism, the traditional trading mechanism is also applicable. the framework of the proposed mechanism is presented from four aspects, including the description, clearing process, operation mode, and linkage between two sub-markets. Then, a market clearing model of the proposed mechanism is built with several traditional transaction modes as special cases of the presented double-market parallel transactions. Finally, taking the centralized transaction as an example, results show that the proposed mechanism can effectively provide market entities more chances to win contracts, and enhance the market liquidity.