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In an open electricity market, generation companies (GENCO) have to optimally bid to gain more profits with incomplete information of other competing generators. In this structure, market participants must develop their bids in order to maximize their profits. Building optimal bidding strategies for GENCO could need to evaluate some market parameters such as forecasting market-clearing price (MCP), non-convex production cost function and forecasting load. A new framework to build bidding strategies for GENCO in an electricity market is presented in this paper. A normal probability distribution function (PDF) is used to describe the bidding behaviors of other competing generators. Bidding strategy of a generator for each trading period in a day-ahead market is solved by a new adaptive particle swarm optimization (APSO). APSO can dynamically follow the frequently changing market demand and supply in each trading interval. A numerical example serves to illustrate the essential features of the approach and the results are compared with the solutions by other PSO algorithms.