We report the frequency measurements of the transitions in at 588 nm using an optical frequency comb stabilized laser system. The Doppler-free spectra of the transitions are demonstrated in an rf discharged sealed-off helium cell using intermodulated fluorescence spectroscopy. The measured absolute frequency of the transition is 510 059 755.352(28) MHz, which is more precise than the previous measurement by two orders of magnitude. The ionization energies of the and states can be derived from our result and agree very well with the previous experimental values. More importantly, the Lamb shift of the state can be deduced to be 4057.086(34) MHz, which is two times more precise than the previous result. In addition, the absolute frequencies of the 2P30,1/2→3D31,3/2, 2P30,1/2→3D31,1/2, and transitions in are measured. Our precision surpasses the theoretical calculations by more than one to two orders of magnitude. The hyperfine separations of the states in and the frequency differences between and transitions are also presented.