Human skin imperfectly discriminates between pressure and temperature stimuli under mixed stimulation, and exhibits nonlinear sensitivity to each stimulus. Despite great advances in the field of electronic skin (E-skin), the limitations of human skin have not previously been overcome. For the first time, the development of a stimulus-discriminating and linearly sensitive bimodal E-skin that can simultaneously detect and discriminate pressure and temperature stimuli in real time is reported. By introducing a novel device design and using a temperature-independent material, near-perfect stimulus discriminability is realized. In addition, the hierarchical contact behavior of the surface-wrinkled microstructure and the optimally reduced graphene oxide in the E-skin contribute to linear sensitivity to applied pressure/temperature stimuli over wide intensity range. The E-skin exhibits a linear and high pressure sensitivity of 0.7 kPa(-1) up to 25 kPa. Its operation is also robust and exhibits fast response to pressure stimulus within 50 ms. In the case of temperature stimulus, the E-skin shows a linear and reproducible temperature coefficient of resistance of 0.83% K-1 in the temperature range 22-70 degrees C and fast response to temperature change within 100 ms. In addition, two types of stimuli are simultaneously detected and discriminated in real time by only impedance measurements.