Energy Internet is one of the key means to realize the energy revolution. However, its characteristics of multiple kinds of energy complementing will increase the complexity of energy supply and thus affect the coordination and order of the system energy supply in the region. This paper carries out the research on the system planning of energy supply network in a certain region. Considering the comprehensive cost of investment, operation, economy and environment as the objective function, it establishes the planning model of regional power supply network considering multiple constraints of power grid and heat supply network and the energy complementary of electric and heat. The model is then solved by Gaussian quantum-behaved PSO algorithm. The regional energy planning of some outskirts of a city in North China is taken as a case of energy supply network planning and compared with traditional planning model. The conclusion shows that the method proposed is able to make planning for regional energy supply network, which contains coal-fired power, pneumoelectric and thermal power at least. Besides, the G-QPSO algorithm used in this paper has a good performance in solving this kind of planning problem; therefore, it has a promising perspective of application. This work is supported by Science and Technology Project of State Grid Corporation of China:Research on the Implementation Scheme and Support System of Electric Power Service Platform under the Situation of New Electricity Reform.