A characteristic-based constrained interpolation profile (CIP) method for solving three-dimensional, time-dependent Maxwell's equations is successfully developed. It is utilized to solve one-dimensional wave equations in the formulation of the Maxwell's equations. Calculation procedure of the CIP method for three-dimensional scattering analysis is described in details. Update equations for boundary conditions of a perfectly conducting (PEC) interface and a dielectric interface are formulated and obtained in explicit forms. Numerical analyses of electromagnetic scatterings of PEC sphere, dielectric sphere and PEC cube are performed and the scattering coefficient is calculated and compared with the Mie's analytic results. As a result, the scattering coefficients show good agreement with the Mie's results, which demonstrates the validity of the CIP method and the formulated update equations. It is also shown that the phase of the scattering coefficients determined by the CIP method are slightly more accurate than that of the FDTD method.