An　all-optical　microwave　photonic　frequency　downconverter　with　tunable　full　range　continuous　phase　shift　is　presented.　In　the　proposed　system,　the　radio　frequency　(RF)　and　local　oscillator　(LO)　signals　modulate　two　sub　Mach-Zehnder　modulators　(MZMs)　in　an　integrated　dual-parallel　MZM　(DPMZM),　respectively.　The　two　sub-MZMs　are　both　biased　at　the　minimum　transmission　point　to　implement　the　carrier-suppressed　double-sideband　modulation.　An　optical　bandpass　filter　is　then　used　to　retain　the　+1st　order　RF　and　LO　sidebands.　When　the　two　sidebands　are　send　to　a　photodetector,　an　intermediate　frequency　(IF)　signal　is　produced,　and　the　phase　of　the　converted　IF　signal　is　linearly　changed　by　adjusting　the　bias　voltage　of　the　parent　MZM　in　the　DPMZM.　An　experiment　is　carried　out.　An　RF　signal　can　be　downconverted　to　a　phase-tunable　IF　signal,　and　the　measured　spurious-free　dynamic　range　reaches　100.2　dB.Hz(2/3).　The　phase　deviation　and　power　ripple　of　the　IF　signal　are　less　than　2　degrees　and　0.26　dB,　respectively.　The　all-optical　design　makes　the　system　bandwidth　unlimited　by　electrical　components.　Meanwhile,　since　the　proposed　microwave　photonic　link　can　simultaneously　implement　frequency　downconversion　and　full　range　phase　shift　of　the　converted　IF　signal,　it　provides　a　compact　alternative　for　the　applications　including　radio-over-fiber　system　and　phased-array　beamforming.