This paper presents a new analytical solution method for Supply Function Equilibrium (SFE)-based bidding strategy in electricity markets. It is assumed that every generation company (GenCo) has some generation units and bids a linear supply function (LSF) for each of its units to the independent system operator (ISO). The problem is modeled as a bi-level optimization problem; in inner level, ISO clears the market to maximize social welfare, and in outer level, each GenCo tries to maximize its individual welfare. The proposed method is used to solve the outer level problem using an iterative algorithm, in which LSF coefficients are parameterized. The formulation is developed for both elastic and non-elastic demands for single and multi-generator cases and also for integrated energy and spinning reserve (SR) markets with three models of competitions: a-, b- and k-parameterization. Three sample networks are used to evaluate the proposed method. The results show that the proposed method is effective, and accurate for GenCos’ strategic bidding in electricity markets compared with other optimization algorithms.