A novel experiment, aiming at demonstrating the feasibility of hypernuclear spectroscopy with heavy-ion beams, was conducted. Using the invariant mass method, the spectroscopy of hypernuclear products of 6Li projectiles on a carbon target at 2 AGeV w
as performed. Signals of the Lambda-hyperon and 3Lambda H and 4Lambda H hypernuclei were observed for final states of p+pi^-, 3He+pi^- and 4He+pi^-, respectively, with significance values of 6.7, 4.7 and 4.9sigma. By analyzing the proper decay time from secondary vertex distribution with the unbinned maximum likelihood fitting method, their lifetime values were deduced to be $262 ^{+56}_{-43} pm 45$ ps for Lambda, $183 ^{+42}_{-32} pm 37$ ps for 3Lambda H, and $140 ^{+48}_{-33}pm 35 $ ps for 4Lambda H.
