The primary issues for the popularization of electric vehicles are low energy density, short life, high cost, and long charging time of battery. In an extended-range electric vehicle, a range-extender is applied to realize the on-board electricity generation avoiding the range anxiety; and a large capacity battery and public charging facilities are not necessary. A primary issue is lack of an efficient range-extender that is light, compact and silent. The main reasons are that the efficiencies of range-extended engines now available are low; and the efficiency optimum operating points of the range-extended engines and generators are not matched. A 3-cylidner gasoline spark-ignition engine for an application in a range-extender has been investigated. Atkinson cycle, exhaust gas recirculation and gasoline direct injection are applied to suppress the knocking. At most cases, a range-extender engine has only a most frequent operating point. All design parameters and operating variables of the range-extender engine can be optimized around the single operating point to maximize the efficiency while matching to the highest efficiency point of a range-extender generator. For this purpose, an optimization and matching method by combing artificial neural network and genetic algorithm has been investigated. The optimization and matching for a range-extender engine, with no generator constraint and with three different constraints of generator efficiency maps, have been conducted. The results show that both the operating points and the optimal parameters of the range-extender engine are different under the different generator constraints. A higher maximum thermal efficiency of the range-extender engine can be achieved as the power requirement decreases. The maximum efficiency of the range-extender engine can reach 40.2%, which is because of the application of high geometrical compression ratio, exhaust gas recirculation, Atkinson cycle and single-point optimization of all parameters.