This paper suggests the transmission of secure speech signals through the MIMO-OFDM system over a doubly selective fading channel. The two-dimensional chaotic map like logistic (TDLM), standard (TDSM), and triangle function combination discrete chaotic map (TD-TFCDM) are used to generate pseudo-random bit generator (PRBG) and index permutation (IP) to encrypt the information based on ciphering and scrambling techniques. Different speech quality and residual intelligibility measures including log-likelihood ratio (LLR), frequency-weighted segmental signal-to-noise ratio (fwSNRseg), signal-to-noise ratio loss (SNRLOSS), correlation coefficient (CC) and spectrogram measures as well as Bit Error Rate (BER) performance are used to test the performance of the proposed security system. The simulation results show that the speech signal over the MIMO-OFDM system behaves well with high security. Also, the speech encryption system using TDSM and TD-TFCDM outperforms TDLM in most residual intelligibility measures.