The electrical characteristics of fiber reinforced plastics (FRP) composites have been investigated in order to develop the self-diagnosis function suitable for health monitoring of structural materials. The electrical conductivity was achieved by adding carbon particles or fiber as a conductive phase into FRP. The self-diagnosis function of the composites was evaluated by the measurement of change in electrical resistance as a function of stress or strain in tensile tests. The resistance of carbon fiber in the composite slightly changed at a small strain level and increased nonlinearly with the applied stress due to the fracture of carbon fiber. The conductive FRP composite containing carbon particles had high sensitivity and linear response of the resistance in a wide strain range. In the cyclic loading tests, the phenomenon of residual resistance was observed at an unloading state in the composites with carbon particles. The residual resistance increased with an applied maximum strain, showing that the composite with carbon particles possesses the function to memorize the applied maximum strain or stress. These results indicate that the FRP composite containing carbon particles has a promising possibility for simple diagnosis of dynamic damage and for damage hysteresis with high sensitivity.