A stochastic analysis of a tension leg platform subjected to wave and current loads is performed. The viscous force is modeled by the nonlinear Morison equation drag force term. As an improvement to equivalent stochastic linearization of the drag force, an equivalent stochastic “quadratization” method is proposed, in which the drag force nonlinearity is replaced by an “equivalent” quadratic nonlinearity. The resulting nonlinear equivalent system is in a form which can be solved approximately by a Volterra series expansion. The non-Gaussian probability distribution of the response is approximated by a Gram-Charlier expansion. The method is applied on a three degree-of-freedom model. The power spectrum of the response determined by the proposed method compares well with the one obtained by a Monte-Carlo simulation.