  We explored a new dark fluid model in the early universe to relieve the
Hubble tension significantly, that tension is the different result of the
Hubble constant derived from CMB inference and local measurements within the
LambdaCDM. We discussed an exponential form of the equation of state in the
acoustic dark energy for the first time, in which gravitational effects from
its acoustic oscillations can impact the CMB phenomena at the epoch of matter
radiation equivalent, called the exponential acoustic dark energy (eADE). And
the constraints were given by the current cosmological data and the comparison
of the phenomena with the stander model was shown through CMB and matter power
spectra. The result shows our model has the $H_0 = 71.65^{+1.62}_{-4.4}$ in 68%
C.L. with a smaller best fitted chi^2 value than that in LambdaCDM.
