We report an experimental investigation of quantum correlations in a two-qutrit spin system in a single nitrogen-vacancy center in diamond at room temperatures. Quantum entanglement between two qutrits was observed at room temperature and the existence of non-classical correlations beyond entanglement in the qutrit case has been revealed. Our work demonstrates the potential of the NV centers as the multi-qutrit system to execute quantum information tasks and provides a powerful experimental platform for studying fundamental physics of high-dimensional quantum systems in future.