The authors describe an algorithm for solving the inverse scattering electromagnetic problem in 3D. Starting with Maxwell's equations and considering a time-harmonic electromagnetic plane wave incident upon a medium enclosed by a bounded domain in \(\mathbb R^3\), they present an iterative linear algorithm for constructing a scatterer embedded in that medium from measurements on the boundary. The algorithm is a continuation of a 2D algorithm, presented in references [\textit{G. Bao} and \textit{J. Lin}, SIAM J. Sci. Comput. 25, No. 3, 1102--1117 (2003; Zbl 1048.65058), \textit{Y. Chen}, Inverse Probl. 13, No. 2, 253--282 (1997; Zbl 0872.35123)] in the text, which requires multi-frequency scattering data. Numerical results are presented showing stability and efficiency for solving the inverse scattering problem.