We employed time-resolved simultaneous small- and wide-angle X-ray scattering (SAXS/WAXS) measurements in combination with a temperature-jump (T-jump) installment to investigate alpha'-to-alpha transition in poly(L-lactide acid) (PLLA) crystals during isothermal annealing at a high temperature. Upon heating in a short period (ca. 10s) to the annealing temperature 150 degrees C, the melting within the pre-existing alpha'-crystal domains before recrystallization into neighboring alpha-crystals was observed, appearing as discontinuous first order alpha'-to-alpha transition, which confirms the melting-recrystallization mechanism co-existing with continuous crystal perfection. Furthermore, during alpha'-to-alpha transition the loosely packed 10/3 helices of alpha'-crystals reorganized into the stable acrystals by extending the lateral crystal sizes rather than the lamellar thickness. Based on our structural characterization, the microscopic mechanism of alpha'-to-alpha transition in PLLA crystals was proposed and approved by dynamic Monte Carlo simulations.