Given two probability distributions, the classical theorem of optimal transport aims to determine a transport plan which can map one distribution to the other such that the transport cost is minimized. The general functions such as seismic traces do not satisfy all properties of probability distribution. Therefore, we normalize the seismic traces by an exponential function prior to applying the optimal transport to define the distance between seismic traces. In this abstract, we report some results of full waveform inversion from an alternative misfit function based on entropy regularized optimal transport. The regularization gives a smooth approximation to the original optimal transport and the regularized optimum can be found efficiently though. Numerical examples demonstrate the proposed misfit function can invert the data with super lower frequency unavailable from a rough initial model.