Swarm intelligence (SI) is a kind of intelligence mode enlightened by some intelligent colony behaviors in nature. This paper focuses on the characteristics of global convergence of genetic algorithm (GA) and particle swarm optimization (PSO) in SI and the strategy of parameter tracking (PT), and fusing them together effectively forms a new algorithm that can solve complex transcendental equations accurately in electromagnetic field. In the process of developing the algorithm, the searching area is decreased, solution is simplified, and the calculating speed is accelerated due to the PT. Moreover, the precision of the results is enhanced due to the dynamic searching area. The predicting of the new searching center by using 3-order difference formula speeds up the calculation further. Based on the developed algorithm, some classical eigenvalue equations that are complex transcendental ones are solved. The computing results show that the algorithm can suitably solve the multi-root problem of complex transcendental equations. Furthermore, the computing result is complete and accurate, and the algorithm is robust. Copyright © 2009 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.