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.
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