Summary The study of vortex-induced vibration (VIV) characteristics of deepwater drilling risers is of great significance for correctly evaluating the risers’ fatigue life. Aiming to determine the VIV response of a deepwater drilling riser under the combined action of the heave motion of the floating drilling platform and sea current, this study established a mechanical model and governing equation of crossflow vortex-parametric vibration (CFVPV) based on the Van der Pol wake oscillator and Euler-Bernoulli beam. For this model, the governing equation is discretized in the time domain by applying the finite element method (FEM), and the equivalent integral form of the differential governing equation is obtained by the Galerkin method, and then solved using the Newmark method. On this basis, the influence of both the heave motion of the floating drilling platform, including the top tension fore, amplitude, and frequency, and the current profile on the CFVPV are analyzed in detail. The results show that the mechanical model and analysis method can be used to assess the CFVPV of deepwater drilling risers with high calculation accuracy. When considering the heave motion, the amplitude of the CFVPV response increases significantly, and more components of the vibration frequency appear. Moreover, the CFVPV displacement decreases with the top tension coefficient and heave motion frequency, while increasing with heave motion amplitude. It was found that the heave motion frequency changes the vibration amplitude and mode of the CFVPV, the effect of which was more obvious for the middle and lower parts of the riser. In addition, increasing the flow velocity reduces the effect of the heave motion. Finally, the CFVPV response at both ends of the riser was greater than that at the middle of the riser under the same flow velocity.