Observational constraints on 3-forms dark energy

3-forms are natural candidates for describing the late-time accelerated expansion of the Universe, as they can inherently reproduce a positive cosmological constant when lacking an evolving potential. When such a potential is present, a 3-form field may exhibit either quintessence-like or phantom-like behaviour. In this paper, we consider a late-time effective dark energy model described by a 3-form with a Gaussian potential, stable during the dark-energy-dominated era. We constrain this model observationally by performing a Markov Chain Monte Carlo (MCMC) analysis employing a comprehensive cosmological dataset, including Planck PR4 cosmic microwave background (CMB) data, DESI DR1 baryon acoustic oscillation (BAO) measurements, Pantheon+ Type Ia supernovae data, low-$z$ Cepheid calibrators, and DES Y1 large-scale structure observations. We demonstrate that the 3-form model successfully increases the predicted Hubble parameter of CMB and BAO data from $67.89\pm0.36{\rm km/s/Mpc}$ of $\Lambda$CDM model to $68.29^{+0.56}_{-0.61}{\rm km/s/Mpc}$ by approaching the potential peak at the right time, thus mildly reducing the tension with the late-time observation. Overall, the 3-form field serves as a promising candidate of phantom-like dark energy from both theoretical and observational points of view.