In this paper, we propose a nonlinear Tomlinson-Harashima pre-coding (THP) scheme for nonlinear distortion suppression in direct-detected double sideband (DSB) PAM-4 transmission systems. Based on the traditional THP, the feedback term is modified by introducing nonlinear components. In this way, more accurate feedback can be obtained to mitigate the signal distortions, especially the nonlinear distortions including the signal-to-signal beating interference and nonlinear power series caused by chromatic dispersion and square-law detection. Meanwhile, we also propose to only reserve the nonlinear kernels with adjacent tap products in nonlinear THP, for the purpose of computation complexity reduction. To verify the effectiveness, transmissions of double sideband (DSB) PAM-4 signal in 1550nm window are experimentally demonstrated. Volterra FFE is adopted on the receiver side to suppress linear and nonlinear pre-cursors. We optimize various parameters of hardware and apply appropriate simplification to the nonlinear THP kernels. The results indicate that, the proposed nonlinear THP can lead to up to three folds BER reduction, compared to the conventional linear THP. Finally, with the combination of proposed nonlinear THP and conventional Volterra FFE, we successfully transmit 84-Gbps PAM-4 and 107-Gbps PAM-4 respectively over 80 km and 40 km under the hard decision forward error correction (HD-FEC) threshold of 3.8 × 10-3.