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Electronic skin with high sensitivity, rapid response, and long-term stability has great value in robotics, biomedicine, and in other fields. However, electronic skin still has challenges in terms of sensitivity and response time. In order to solve this problem, flexible electronic skin with high sensitivity and the fast response was proposed, based on piezoresistive graphene films. The electronic skin was a pressure sensor array, composed of a <inline-formula> <math display="inline"> <semantics> <mrow> <mn>4</mn> <mo>&#215;</mo> <mn>4</mn> </mrow> </semantics> </math> </inline-formula> tactile sensing unit. Each sensing unit contained three layers: The underlying substrate (polyimide substrate), the middle layer (graphene/polyethylene terephthalate film), and the upper substrate bump (polydimethylsiloxane). The results of the measurement and analysis experiments, designed in this paper, indicated that the flexible electronic skin achieved a positive resistance characteristic in the range of 0 kPa&#8315;600 kPa, a sensitivity of <inline-formula> <math display="inline"> <semantics> <mrow> <mn>10.80</mn> <mspace width="0.166667em"></mspace> <mi mathvariant="sans-serif">&#937;</mi> </mrow> </semantics> </math> </inline-formula>/kPa in the range of 0 kPa&#8315;4 kPa, a loading response time of 10 ms, and a spatial resolution of 5 mm. In addition, the electronic skin realized shape detection on a regular-shaped object, based on the change in the resistance value of each unit. The high sensitivity flexible electronic skin designed in this paper has important application prospects in medical diagnosis, artificial intelligence, and other fields.