In　this　article,　we　focus　on　investigating　the　optimal　convergence　order　of　error　estimates　for　the　stabilizer-free　weak　Galerkin　finite　element　method　for　a　second-order　time-dependent　differential　equation　under　low　regularity　assumptions.　In　most　of　the　existing　literature　on　stabilizer-free　weak　Galerkin　finite　element　methods,　the　exact　solution　is　usually　assumed　to　have　at　least　H-2　regularity　so　as　to　achieve　convergence　rates.　But　in　many　applications,　the　exact　solution　has　only　H1+gamma　(0　＜　gamma　＜　1)　regularity,　and　hence　the　existing　error　analysis　is　no　longer　applicable.　Our　objective　is　to　build　a　theoretical　framework　for　filling　in　this　gap.　Our　key　idea　is　to　interpolate　an　H-2　approximation　between　the　exact　solution　and　the　stabilizer-free　weak　Galerkin　approximation　as　an　intermediate　auxiliary　step.　Based　on　this,　the　optimal　convergence　order　of　error　estimates　is　proved　to　be　of　1+gamma.　Finally,　we　present　several　numerical　experiments　on　uniform　triangulations　and　square　partitions　to　demonstrate　the　theoretical　convergence　properties.