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Waveform models are important to gravitational wave data analysis. Peoplerecently pay much attention to the waveform model construction for eccentricbinary black hole coalescence. Several Effective-One-Body Numerical-Relativitywaveform models of eccentric binary black hole coalescence have beenconstructed. But none of them can treat orbit eccentricity and spin-precessingsimultaneously. The current paper focuses on this problem. The authorspreviously have constructed waveform model for spin-aligned eccentric binaryblack hole coalescence $\texttt{SEOBNRE}$. Here we extend such waveform modelto describe eccentric spin-precessing binary black hole coalescence. Wecalculate the 2PN orbital radiation-reaction forces and the instantaneous partof the decomposed waveform for a general spinning precessing binary black holesystem in effective-one-body (EOB) coordinates. We implement these resultsbased on our previous $\texttt{SEOBNRE}$ waveform model. We have also comparedour model waveforms to both SXS and RIT numerical relativity waveforms. We findgood consistency between our model and numerical relativity. Based on our newwaveform model, we analyze the impact of the non-perpendicular spincontributions on waveform accuracy. We find that the non-perpendicular spincontributions primarily affect the phase of the gravitational waveforms. Forthe current gravitational wave detectors, this contribution is not significant.The future detectors may be affected by such non perpendicular spincontributions. More importantly our $\texttt{SEOBNRE}$ waveform model, as thefirst theoretical waveform model to describe eccentric spin-precessing binaryblack hole coalescence, can help people to analyze orbit eccentricity and spinprecession simultaneously for gravitational wave detection data.

Effective-One-Body Numerical-Relativity waveform model for Eccentric spin-precessing binary black hole coalescence