  The Hubble tension arises from different observations between the late-time
and early Universe. We explore a new model with dark fluid, called the
exponential Acoustic Dark Energy (eADE) model, to relieve the Hubble tension.
The eADE model gives an exponential form of the equation of state (EoS) in the
acoustic dark energy, which is the first time to explore an exponential form
for the EoS. In this model, the gravitational effects from the acoustic
oscillations of the model can impact the CMB phenomena at the matter radiation
equally epoch. We give the constraints of the eADE model by the current
cosmological dataset. The comparison of the phenomena with the standard model
can be shown through CMB and matter power spectra. The fitting results of our
model have $H_0 = 70.06^{+1.13}_{-1.09}$ in 95$\%$ C.L. and a smaller best-fit
value than $\Lambda$CDM.
