The implementation of the Orthogonal Frequency Division Multiplexing (OFDM) can be achieved using Inverse Discrete Cosine Transform (IDCT), and DCT instead of Inverse Discrete Fourier Transform (IDFT), and DFT. The Carrier Frequency Offset (CFO) is the main issue of the OFDM system. One of the tools to mitigate the CFO effect and improve the Bit-Error-Rate (BER) performance is the equalization procedure. Also, the 1-Dimension (1-D), and 2-Dimension (2-D) burst errors can be mitigated using a chaotic interleaver in the OFDM system. This consequently improves the BER performance. In this paper, we propose a Joint Low-Complexity Regularized Linear Zero Forcing (JLCRLZF) equalizer for the OFDM system based on DCT in addition to a chaotic interleaving scheme. The proposed equalizer depends on the concept of the banded-matrix approximation, and jointly performs the equalization and CFO compensation processes. Simulation results ensure the importance of the proposed JLCRLZF equalizer compared to other algorithms.