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Frequently, we meet characteristic equations in scientific research, and it is very important to get all multiple solutions. A new and effective algorithm combining Genetic Algorithm with Parameter Tracking Scheme is developed. Based on the algorithm, characteristic equations in electromagnetic field can be solved successfully, such as the complex transcendental equation of medium permittivity that is measured by the method of terminal short circuit, the characteristic equation of rectangular waveguide that is filled partially and asymmetrically by magnetic materials and so forth. The computing results have good agreements with known outcomes of these questions obtained by other methods. As compared with other schemes, the algorithm has some advantages, such as initial value and gradient information free, completeness, robustness, generalization, and precision etc.