In this study an indirect statistical method has been proposed to estimate the tsunami hazard assessment along the Alborán Sea Coast (Southeastern Spanish Coast). This method can be summarized as: (1) analysis of the global neotectonic setting, including geodynamic processes as well as seismicity of the region; (2) tsunami source model; (3) generation of a numerical data base of tsunami events using a numerical model; (4) probabilistic model based on Monte-Carlo simulations in order to generate a synthetic tsunami catalogue; and (5) a multidimensional interpolation method applied to combine the numerical data base with the synthetic catalogue to produce inundation maps. The purpose of this study is to establish tsunami-wave elevation at the shoreline versus the return period curves for different locations along the Alborán Sea coast. Furthermore, an inundation map of the city of Roquetas del Mar (Almeria) has been obtained. It is concluded that the tsunamis generated in the Alborán basin have a medium to low hazard, with the most important elevations in the Málaga, Adra and Melilla areas.