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In this work we propose a new coupled generalized three-form dark energymodel, in which dark energy are represented by a three-form field and othercomponents are represented by ideal fluids. We first perform a dynamicalanalysis on the new model and obtain four fixed points, including a saddlepoint representing a radiation dominated Universe, a saddle point representinga matter dominated Universe, and two attractors representing two dark energydominated Universes. We then use the observational data, including cosmicmicrowave background (CMB) data, baryon acoustic oscillations (BAO) data, andType Ia supernovae (SN Ia) data to constrain the model parameters of thecoupled generalized three-form dark energy model. For comparison, we alsoconsider the coupled three-form dark energy model, generalized three-form darkenergy model, and $\Lambda$CDM model, we find that the coupled generalizedthree-form dark energy model is the only one model that can reduce the $H_0$tension to a more acceptable level, with $H_0=70.1_{-1.5}^{+1.4}$ km/s/Mpc,which is consistent with R19 at $2.0\sigma$ confidence level. We alsoinvestigate the best-fit dynamical behavior of the coupled generalizedthree-form dark energy model, and show that our model is equivalent to aquintom dark energy model, in which dark energy, at early epoch, behaves likesome form of early dark energy with a small positive equation of state.

Relieve the $H_0$ tension with a new coupled generalized three-form dark energy model