In recent years use of narratives for teaching science at secondary school level has gained impetus. This paper deals with the problem of designing narratives for teaching scientific concept. The central issue of the problem of designing narratives for carrying scientific information is that science belongs to the domain of objective observation of facts and general principles while narratives belong to the world of humans and their aspirations which are subjective in nature. If a narrative of science is built purely on intuitive bases, without any structural foundation, the epistemic correctness of the narrative may be doubted. This paper presents what is known as the Epistemic Narrative Structure (ENS) which synthesis principles of Narrative structure with general structure of a scientific discovery event. It is proposed that if a narrative about teaching science is built on the epistemic narrative structure, then the problem of synthesizing subjective human context and objective nature of scientific reasoning can be resolved leading to design of epistemologically correct science narratives. In this paper, the Epistemic Narrative Structure is explained and how it can be used to design a science narrative with an example of writing a narrative on 'how electric battery came into being.The narrative structure is replicable and can be used by teachers to design their own epistemologically correct science narratives.