A new diagnosis method for the discriminative detection of laser-accelerated multi-MeV carbon ions from background oxygen ions utilizing solid-state nuclear track detectors (SSNTDs) is proposed. The idea is to combine two kinds of SSNTDs having different track registration sensitivities: Bisphenol A polycarbonate detects carbon and the heavier ions, and polyethylene terephthalate detects oxygen and the heavier ions. The method is calibrated with mono-energetic carbon and oxygen ion beams from the heavy ion accelerator. Based on the calibration data, the method is applied to identify carbon ions accelerated from multilayered graphene targets irradiated by a high-power laser, where the generation of high-energy high-purity carbon ions is expected. It is found that 93 ± 1% of the accelerated heavy ions with energies larger than 14 MeV are carbons. The results thus obtained support that carbon-rich heavy ion acceleration is achieved.