  Waveform models are important to gravitational wave data analysis. People
recently pay much attention to the waveform model construction for eccentric
binary black hole coalescence. Several Effective-One-Body Numerical-Relativity
waveform models of eccentric binary black hole coalescence have been
constructed. But none of them can treat orbit eccentricity and spin-precessing
simultaneously. The current paper focuses on this problem. The authors
previously have constructed waveform model for spin-aligned eccentric binary
black hole coalescence $\texttt{SEOBNRE}$. Here we extend such waveform model
to describe eccentric spin-precessing binary black hole coalescence. We
calculate the 2PN orbital radiation-reaction forces and the instantaneous part
of the decomposed waveform for a general spinning precessing binary black hole
system in effective-one-body (EOB) coordinates. We implement these results
based on our previous $\texttt{SEOBNRE}$ waveform model. We have also compared
our model waveforms to both SXS and RIT numerical relativity waveforms. We find
good consistency between our model and numerical relativity. Based on our new
waveform model, we analyze the impact of the non-perpendicular spin
contributions on waveform accuracy. We find that the non-perpendicular spin
contributions primarily affect the phase of the gravitational waveforms. For
the current gravitational wave detectors, this contribution is not significant.
The future detectors may be affected by such non perpendicular spin
contributions. More importantly our $\texttt{SEOBNRE}$ waveform model, as the
first theoretical waveform model to describe eccentric spin-precessing binary
black hole coalescence, can help people to analyze orbit eccentricity and spin
precession simultaneously for gravitational wave detection data.
