The behavior of a nonlinear dynamic system under arbitrary excitation can be represented by the Volterra series if the Volterra kernels of different orders are known. This study presents a methodology for a direct estimation of the Volterra kernel coefficients up to the second-order using prepared data obtained by running a time-domain analysis of the system of interest. To avoid potential problems during kernel estimation, the Volterra kernel is expanded into a polynomial series using the Laguerre polynomials, and the coefficients of the Laguerre polynomials are then estimated using a least-square method. A nonlinear oscillator with a quadratic stiffness term is introduced, and the methodology is applied to check the applicability and accuracy. The methodology is applied to a more realistic engineering problem of a simplified riser under irregular wave excitation.