Secure communication techniques can protect data confidentiality during transmission through public channels. Chaotic systems are commonly used in secure communication due to their random-like behavior, unpredictability, and ergodicity. However, existing chaos-based secure communication schemes have some drawbacks concerning the chaotic systems used and the communication structures, so they cannot achieve satisfactory performance to resist transmission channel noise. In light of this, in this paper, we propose a two-dimensional (2D) cyclic chaotic system (2D-CCS) and design a novel chaos-based secure communication scheme called noise-reduced orthogonal frequency division multiplexing based differential chaos shift keying (NR-OFDM-DCSK). The 2D-CCS is a general framework that can generate a large number of new 2D chaotic maps using existing one-dimensional (1D) chaotic maps as seed maps. Theoretical analysis and experiment results demonstrate its robust chaotic behaviors. The NR-OFDM-DCSK employs a new chaotic map generated by 2D-CCS as the chaos generator, and its structure exhibits a strong ability to resist channel noise, as demonstrated by formulaic analysis. Our extensive experiments show that our developed 2D chaotic maps are more suitable for secure communication applications than existing 2D chaotic maps, and our NR-OFDM-DCSK can achieve a lower bit-error-rate (BER) than state-of-the-art secure communication schemes.