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Using (2712.4 +/- 14.3) x 10(6) psi(3686) events collected with the BESIII detector at BEPCII, a partial wave analysis of the decay psi(3686) ->phi eta eta' is performed with the covariant tensor approach. In addition to the established states h(1)(1900) and psi(2170), an axial-vector state with a mass near 2.3 GeV/c(2) is observed for the first time. Its mass and width are measured to be 2316 +/- 9(stat) +/- 30(syst) MeV/c(2) and 89 +/- 15(stat) +/- 26(syst) MeV, respectively. The product branching fractions of B[psi(3686) -> X(2300)eta']B[X(2300) ->phi eta] and B[psi(3686) -> X(2300)eta]B[X(2300)phi eta'] are determined to be (4.8 +/- 1.3(stat) +/- 0.7(syst) ) x 10(-6) and (2.2 +/- 0.7(stat) +/- 0.7(syst)) x 10(-6), respectively. The branching fraction B[psi(3686 phi eta eta'] is measured for the first time to be (3.14 +/- 0.17(stat) +/- 0.24(syst) ) x 10(-5). The first uncertainties are statistical and the second are systematic.