A technique to suppress both the second and third order nonlinear distortions in a long-haul microwave photonic link (MPL) is presented. The MPL consists of a dual-polarization dual-parallel Mach-Zehnder modulator (DP-DPMZM), a polarizer, a length of fiber, an optical bandpass filter (OBPF), and a balanced photodetector (BPD). The DP-DPMZM has two sub-DPMZMs. For a two-tone signal at f1 and f2, the second order harmonic distortions (SHD) and the second order intermodulation distortions (IMD2) at f2+f1 are suppressed by biasing one sub-DPMZM to operate with single-sideband suppressed carrier (SSB-SC) modulation. The IMD2 at f2-f1 is suppressed by balanced detection at the BPD. The third order intermodulation distortions (IMD3) are suppressed by adjusting the states of polarization of the light wave into the polarizer. The spurious free dynamic range (SFDR) in a multi-octave band is free from fiber dispersion effect due to the bias setting of the DP-DPMZM. As a result, a high multi-octave SFDR can be obtained irrespective of the transmission distance. The proposed MPL is analyzed theoretically and is verified experimentally. The measured multi-octave SFDR is 95.9 dBHz1/2 and 92.1 dBHz1/2 when a long fiber link at 10 km and 20 km is used for signal transmission, respectively, which is 16.1 dB and 17.3 dB higher compared to a conventional Mach-Zehnder modulator (MZM) based MPL operating under the same condition.