Earthquakes can be viewed as a relaxation process of the earth crust loaded with stresses mainly at the lithospheric plate boundaries. When an earthquake occurs the stress in the crust shall be redistributed generating new earthquakes where and when the stress assume again a value greater than the slipping threshold. This observation leads to study the earthquakes diffusion mechanism. Here we investigate the fluctuations of the average free walk between an earthquake and another, evaluating the scaling of the distance between earthquakes with the waiting time τ. We find scaling exponents varying with the order of the statistical moments and always less than 1. This implies strong anomalous diffusion that we interpret as due to different mechanisms of diffusion depending by the scale.