Time series of the dynamic response of a slender marine structure was predicted using quadratic Volterra series. The wave-structure interaction system was identified using the NARX(Nonlinear Autoregressive with Exogenous Input) technique, and the network parameters were determined through the supervised training with the prepared datasets. The dataset used for the network training was obtained by carrying out the nonlinear finite element analysis on the freely standing riser under random ocean waves of white noise. The nonlinearities involved in the analysis were both large deformation of the structure under consideration and the quadratic term of relative velocity between the water particle and structure in Morison formula. The linear and quadratic frequency response functions of the given system were extracted using the multi-tone harmonic probing method and the time series of response of the structure was predicted using the quadratic Volterra series. In order to check the applicability of the method, the response of structure under the realistic ocean wave environment with given significant wave height and modal period was predicted and compared with the nonlinear time domain simulation results. It turned out that the predicted time series of the response of structure with quadratic Volterra series successfully captures the slowly varying response with reasonably good accuracy. It is expected that the method can be used in predicting the response of the slender offshore structure exposed to the Morison type load without relying on the computationally expensive time domain analysis, especially for the screening purpose.