The existence of extrema, maximum and/or minimum and negative gradients of melting curves observed for several elements at high pressure is investigated by molecular dynamics simulation using the two-species model (TSM) proposed by Ogura et al. [1]. TSM is a model which imitates the change in the electronic structure of an atom in terms of a species change in particles. The TSM phase diagram has two solid phases and one liquid phase with a solid-solid-liquid triple point which corresponds to the melting curve minimum. The melting curve has both a maximum and a minimum, and the gradient of the melting curve is negative between these extrema. These peculiar melting curve properties and phase diagram are common to alkali metals and some other elements.