In this study, we investigated the quasi-periodicity of large avalanches using a new modification of sandpile models, i.e., the long-range connective sandpile (LRCS) model. The LRCS model considers the random distant connection between two separated, instead of neighboring, cells and shows interesting precursory behavior before large avalanches. We explore the statistics of recurrence intervals between large events and find a strong dependence on the size L of the sandpile. In the LRCS model, the average recurrence interval W of large avalanches follows the relationship W ∝ L2.07. Having the recurrence intervals of many earthquake fault systems around the world, we propose an empirical rule between those intervals and the corresponding earthquakes' magnitudes and provide evidence of the quasi-periodic behavior of natural earthquakes.