The process e+e−→ϕΛ¯Λ is studied using data samples collected with the BESIII detector at the BEPCII Collider at center of mass energies √s ranging from 3.51 GeV to 4.60 GeV. An enhancement is observed near the threshold of Λ¯Λ. The lineshape of this enhancement is studied in different approaches, including fit with a Breit-Wigner function or a reversed exponential function. The Breit-Wigner function has a mass of (2262±4±28) MeV/c2 and a width of (72±5±43) MeV, where the quoted uncertainties are statistical and systematic, respectively. The rising rate of the reversed exponential function is measured as 33±11±6 MeV/c2. For the Λ¯Λ system, the JPC quantum numbers of 0−+ and 0++ are rejected, while other JPC hypotheses are possible, according to the helicity-angle study. The energy-dependent cross section of the e+e−→ϕΛ¯Λ process is measured for the first time in this energy region, and contributions from excited ψ states and vector charmoniumlike Y-states are investigated.