Abstract: Recent heavy ion experiments (HypHI, STAR) announced surprisingly short lifetime for _Λ³H mesonic weak decay (MWD), which is difficult to interpret given the fact that _Λ³H is a very loosely bound system. This intriguing issue is known as hypertriton lifetime puzzle. In order to test the lifetime of the hypertriton with different experimental methods, we propose to use the K^-beam of J-PARC to measure the lifetime of the hypertriton through the reaction channel of K^-+ ³He → _Λ³H + π⁰. In this article, we will summarize the situation and introduce some recent activities aiming at solving this puzzle. Our method will not suffer from the track reconstruction efficiency as the heavy ion based experiments; thus provide an important test for the hypertriton lifetime puzzle with comparable precision.