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Worldwide, the majority of small islands not connected to the main grid is still dependent on fossil fuels. From an economic and environmental point of view, this condition is no more sustainable given the high costs for electricity generation and the high level of pollutant emissions. Furthermore, the dependence on fossil fuel represents a risk for the security of the supply of several small developing Countries since they are obliged to import those resources from foreign Countries. The introduction of renewable energy sources in small islands represents a valid solution to solve these problems. In this context, the paper investigates the case of Lampedusa, a small Italian island whose electrical power system is currently totally supplied by diesel power plants. In the paper, the authors investigate the transition toward an economically and technically feasible generating system based on solar, wind and sea wave plants, to achieve specific targets of decarbonization. Commercial technologies are adopted for the exploitation of solar and wind sources, while sea wave plants are based on an innovative device, currently under development at the University of Palermo. A mathematical model is proposed to find the optimal energy mix that can satisfy a fixed share of annual electricity production from renewables, considering the Levelized Cost of Electricity. Finally, the proposed solution is analyzed in order to check the dynamic stability of the power system. The paper shows that, for replacing the 40% of the current electricity demand of Lampedusa, an optimal energy mix comprising 1509 kW from photovoltaic plants, 2100 kW from wind turbines and 640 kW from wave energy converters is needed. In this way, the actualized cost for the electricity production could be reduced to 0.260 €/kWh from the current value of 0.282 €/kWh.