We report on the results of a new spectroscopic monitoring campaign of the quasar PG 0026+129 at the Calar Alto Observatory 2.2m telescope from July 2017 to February 2020. Significant variations in the fluxes of the continuum and broad-emission lines, including H$beta$ and He II, were observed in the first and third years, and clear time lags between them are measured. The broad H$beta$ line profile consists of two Gaussian components: an intermediate-width H$beta_{rm IC}$ with a full width at half-maximum (FWHM) of 1964$pm$18 $rm km~s^{-1}$ and another very broad H$beta_{rm VBC}$ with a FWHM of 7570$pm$83 $rm km~s^{-1}$. H$beta_{rm IC}$ has long time lags of $sim$40--60 days in the rest frame, while H$beta_{rm VBC}$ shows nearly zero time delay with respect to the optical continuum at 5100 AA. The velocity-resolved delays show consistent results: lags of $sim$30--50 days at the core of the broad H$beta$ line and roughly zero lags at the wings. H$beta_{rm IC}$ has a redshift of $sim$400 $rm km~s^{-1}$ which seems to be stable for nearly 30 years by comparing with archived spectra, and may originate from an infall. The root mean square (rms) spectrum of H$beta_{rm VBC}$ shows a double-peaked profile with brighter blue peak and extended red wing in the first year, which matches the signature of a thin disk. Both the double-peaked profile and the near-zero lag suggest that H$beta_{rm VBC}$ comes from a region associated with the part of the accretion disc that emits the optical continuum. Adopting the FWHM (in the rms spectrum) and the time lag measured for the total H$beta$ line, and a virial factor of 1.5, we obtain a virial mass of $2.89_{-0.69}^{+0.60} times10^7 M_{odot}$ for the central black hole in this quasar.
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