A multi-octave highly-linear analog photonic link with simultaneous suppression of second-order intermodulation distortion (IMD2) and third-order intermodulation distortion (IMD3) is proposed and demonstrated based on a single integrated polarization-multiplexing dual-parallel Mach-Zehnder modulator (PM-DPMZM). The IMD2 is eliminated by biasing one sub-MZM in each sub-DPMZM at a point close to the maximum transmission point and the other sub-MZM at a point close to the minimum transmission point. The obtained fundamental frequency terms are in phase while the second-order harmonics are complementary when the two outputs of the two sub-MZMs are photodetected. The IMD3 is suppressed by adjusting the RF powers introduced to the two sub-DPMZMs, producing two complementary IMD3 terms when the modulated signals are photodetected. An experiment is carried out. Simultaneous suppression of IMD2 and IMD3 is achieved. The second-order spurious-free dynamic range (SFDR2) and third-order spurious-free dynamic range (SFDR3) are 82 dB·Hz1/2 and 110 dB·Hz2/3, respectively, indicating an improvement of 12 dB in SFDR2 and 13 dB in SFDR3 as compared with the low-biased MZM based analog photonic link, or an improvement of 3 dB in SFDR2 and 16 dB in SFDR3 as compared with the quadrature-biased MZM based photonic link.