Due to improvements in the sensitivity of gravitational wave(GW)detectors,the detection of GWs originating from the fundamental quasi-normal mode(f-mode)of neutron stars has become possible.The future detection of GWs originating from the f-mode of neutron stars will provide a potential way to improve our understanding of the nature of nuclear matter inside neutron stars.In this work,we investigate the constraint imposed by the f-mode oscillation of neutron stars on the symmetry energy of nuclear matter using Bayesian analysis and parametric EOS.It is shown that if the frequency of the f-mode of a neutron star of known mass is observed precisely,the symmetry energy at twice the saturation density(Esym(2ρ0))of nuclear matter can be constrained within a relatively narrow range.For example,when all the following parameters are within the given intervals:220≤K0≤260 MeV,28≤Esym(ρ0)≤36 MeV,30≤L≤90 MeV,-800≤J0≤400 MeV,-400≤Ksym≤100 MeV,-200≤Jsym≤800 MeV,Esym(2ρ0)will be constrained to within 48.8-5.5+6.6 MeV if the f-mode frequency of a canonical neutron star(1.4 M☉)is observed to be 1.720 kHz with a 1%relative error.Furthermore,if only f-mode frequency detection is available,i.e.there is no stellar mass measurement,a precisely detected f-mode frequency can also impose an accurate constraint on the symmetry energy.For example,given the same parameter space and the same assumed observed f-mode frequency mentioned above,and assuming that the stellar mass is in the range of 1.2-2.0 M☉,Esym(2ρ0)will be constrained to within 49.5-6.8+8.1 MeV.In addition,it is shown that a higher slope of 69≤L≤143 MeV will give a higher posterior distribution of Esym(2ρ0),53.8-6.4+7.0 MeV.