Artificial skin, which mimics the functions of natural skin, will be very important in the future for robots used by humans in daily life. However, combining skin's pressure sensitivity and mechanical self-healing properties in a man-made material remains a challenging task. Here, we show that graphene and polymers can be integrated into a thin film which mimics both the mechanical self-healing and pressure sensitivity behavior of natural skin without any external power supply. Its ultimate strain and tensile strength are even two and ten times larger than the corresponding values of human skin, respectively. It also demonstrates highly stable sensitivity to a very light touch (0.02 kPa), even in bending or stretching states.