Multi-carrier continuous-variable quantum key distribution (CV-QKD) is considered to be a promising way to boost the secret key rate (SKR) over the existing single-carrier CV-QKD scheme. However, the extra excess noise induced in the imperfect multi-carrier quantum state preparation process of N subcarriers will limit the performance of the system. Here, a systematic modulation noise model is proposed for the multi-carrier CV-QKD based on the orthogonal frequency division multiplexing (OFDM). Subsequently, the performance of multi-carrier CV-QKD with arbitrary modulation protocol (e.g. QPSK, 256QAM and Gaussian modulation protocol) can be quantitatively evaluated by combining the security analysis method of the single-carrier CV-QKD. Under practical system parameters, the simulation results show that the SKR of the multi-carrier CV-QKD can still be significantly improved by increasing the carrier number N even with imperfect practical modulations. Specifically, the total SKR of multi-carrier CV-QKD can be optimized by carefully choosing N. The proposed model provides a feasible theoretical framework for the future multi-carrier CV-QKD experimental implementation.