The usage of numbers generated by true random number generators is critical in cryptology field due to security reasons. On the other hand, generated raw numbers rarely have good statistical properties because entropy sources used in true random number generators can be influenced by environmental factors. Post-processing is required for TRNGs to overcome the shortcomings of generated raw numbers. In this paper, a chaos-based post-processing technique is proposed as an alternative to other post-processing techniques in the literature. Logistic map is used in post-processing to ensure that numbers generated by RO-based TRNG are high quality. Four different scenarios considering RO-based TRNG structure are examined in order to observe the effects of the logistic map. The proposed system is set on EP4CE115F29C7-based Altera FPGA board, and the statistical properties of generated numbers are tested according to NIST 800.22 test suit and TESTU01. The degree of non-periodicity of the developed system was inspected by employing scale index method. The generated series pursuant to the obtained results was non-periodic. The results suggest that logistic map can be used as post-processing.