A high-linearity directly-modulated analog photonic link (APL) with simultaneous suppression of the even-order intermodulation distortion, third-order intermodulation distortion (IMD3), and cross-modulation distortion (XMD) is proposed and experimentally demonstrated by the corporation of push–pull structure and an adaptive compensation algorithm. In the proposed directly-modulated APL system, the push–pull structure is introduced to effectively eliminate all the even-order nonlinear distortions, including the second-order intermodulation distortion and the second-order harmonic distortions. To further simultaneously suppress the IMD3 and XMD, an adaptive compensation algorithm is designed and adopted at the receiver. The experimental results show that the second-order spurious-free dynamic range and the third-order spurious-free dynamic range is improved by 19.8 and 12.4 dB, respectively, corresponding to 7.15% error vector magnitude performance improvement for a 120 Mb/s 64QAM-OFDM RF signal transmission when the input RF power is 13 dBm.