Statistical study of earthquakes in the past, due to the small-medium size magnitude earthquake associated with surface rupture are rare, considers that only the earthquakes beyond magnitude 6 1/2 could produce surface ruptures in the most cases. Identification of paleoseismic events is also often based on this assumption. In this paper, we summarized 56 historical moderate size earthquakes worldwide, which have clearly documented about surface ruptures from 1950 to 2014.Results show that the magnitude lowest limit of the earthquake associated with surface rupture may be lower than the 6 1/2 , probably is about 5, even can be as low as 3.6 under extreme conditions. Additionally, from the view of theory and practice, this paper explored the effect of control factors on surface rupture, so as to indicate that the shallow focal depth is one of the most important factors for small-medium size earthquake associated with surface rupture, also included are the high heat flow values, tensile tectonic environment and active fault with weak friction strength. Although the probability that small magnitude earthquake produces surface rupture is low, it is not impossible. In the interpretation of paleoearthquake events, it also cannot overgeneralize that the corresponding earthquake magnitude must be 6.5 or greater as long as the fracture appeared, while ignoring the possibility of some moderate size earthquakes.