A time-resolved spectroscopy method combined with pulse electron excitation are used for the experimental investigation of the quenching process of He excited states by collisions with nitrogen molecules in a He–Ne–N2 mixture at low pressure. The rate constants for quenching 4He(21S), 4He(21P), 3He(21S) and 3He(21P) states by collisions with ground state N2 molecules at Tg=600K are: k=(2.66±0.09)×10-10 and k=(1.89±0.28)×10-9cm3s-1 for 4He(21S) and 4He(21P), respectively, and k=(2.81±0.07)×10-10 and k=(3.21±0.58)×10-9cm3s-1 for 3He(21S) and 3He(21P), respectively.