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In polistic electricity market structure, each power producers can maximise its profit through bidding strategy. Also, with the advent of renewable generation mostly wind has shaped a new prospect in the bidding process. Although, the wind power output uncertainty, wind power suppliers facing an inevitable uncertainty problem in an emerging power market. To alleviate the adverse impact of this uncertainty on wind power bidding, Weibull distribution is used to model wind power scenarios and the forward‐reduction algorithm is utilised to reduce scenarios. Furthermore, an overestimation and underestimation cost function is modelled to measure the deviation of wind power output. The bidding strategy with the inclusion of wind power is proposed in this study to maximise profit. However, the uncertainty of rival's behaviour affects the bidding process, which minimised by utilising the normal probability distribution function. The proposed problem is tested on the IEEE standard 30‐bus and 57‐bus systems and solved by the gravitational search algorithm (GSA). The results are obtained without and with wind power and shows that the effects of wind power on market clearing price and bidding strategy. Moreover, GSA gives higher market clearing price and net profit as compared with particle swarm optimisation and genetic algorithm.