The near-threshold $e^+e^- to Lambdabar{Lambda}$ reaction is studied with the assumption that the production mechanism is due to a near-$Lambda bar{Lambda}$-threshold resonance. The cross section of $e^+e^- to Lambdabar{Lambda}$ reaction is parametrized in terms of the electromagnetic form factors of $Lambda$ hyperon, which are obtained within the vector meson dominance model. It is shown that the contribution to the $e^+e^- to Lambdabar{Lambda}$ reaction from a new narrow state with quantum numbers $J^{PC}=1^{--}$ is dominant for energies very close to threshold. The mass of this new state is about 2232 MeV, which is very close to the mass threshold of $Lambda bar{Lambda}$, while its width is just a few MeV. This solves the problem that all previous calculations seriously underestimate the near-threshold total cross section of the $e^+e^- to Lambdabar{Lambda}$ reaction.
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