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Electromagnetic Tomography (EMT) reconstructs the media distribution by making boundary measurements. Calculation of eddy current field is an important step in solving the forward and inverse problems for Electromagnetic Tomography (EMT). This paper reports a novel, fast eddy current solver by exploiting the negligibly coupled field approximation. Presently, calculation of eddy current field based on full wave equations has generally been achieved by using commercial software such as COMSOL or ANSOFT, and they are often time-consuming and memory-consuming. In this paper, a novel solution, based on the negligibly coupled field approximation, is developed and proves flexible and much faster. Five numerical experiments were designed to test and verify the accuracy of this software, and the results were completely consistent with the theoretical analysis.