  We consider a specific dark energy model, which only includes the Lagrangian
up to the cubic order in terms of the vector field self-interactions in the
generalized Proca theory. We examine the cosmological parameters in the model
by using the data sets of CMB and CMB+HST, respectively. In particular, the
Hubble constant is found to be $H_0=71.80^{+1.07}_{-0.72}$
($72.48^{+0.72}_{-0.60}$) $\rm kms^{-1}Mpc^{-1}$ at $68\%$~C.L. with CMB
(CMB+HST), which would alleviate the Hubble constant tension. We also obtain
that the reduced $\chi^2$ values in our model are close to unity when fitting
with CMB and CMB+HST, illustrating that our model is a good candidate to
describe the cosmological evolutions of the universe.

General Relativity and Quantum Cosmology;Cosmology and Nongalactic Astrophysics