We present a completely analytical vortex-fluid model describing several vortex-fluid phases of hole-doped cuprate superconductors below and above T c. A key feature of the model is to synthesize several vortex damping mechanisms of scattering inside vortex core, core–core collisions and pinning. Accurate predictions for both magnetoresistance and Nernst effect are obtained, validated by measurements in six Bi-based cuprate samples over a wide range of temperature and magnetic fields, which strongly support the phase-fluctuation scenario in Bi-based cuprates. The model quantifies the unconventional vortex properties by a set of physical parameters, which adds quantitative contents to the discussions of pseudogap. A speculation is offered to use the vortex-fluid model as a first step towards achieving a comprehensive understanding of Nernst effect for all HTSC.