Poly(L-lactic acid) (PLLA) is a biodegradable plastic and one of the most famous plastics made from biobased materials. However, its physical strength is insufficient compared to general-purpose plastics. In this study, the effect of methylcyclodextrin (MeCD) addition on the structure and physical properties, especially the drawing behavior, of PLLA was investigated. Through thermal analysis, it was found that MeCD addition lowers the crystallinity and enhances the mobility of PLLA. The sample containing approximately 17% MeCD was drawn to more than 1000% at 60 °C, although PLLA fractured at a strain of less than 100%. Differential scanning calorimetry (DSC)-Raman in situ measurements also revealed decreases in the glass transition temperature (T g), cold crystallization temperature (T c), and melting point (T m), and improvement in structural distribution with temperature. DSC-Raman measurements simultaneously supplied information about crystallinity and thermal properties. Thus, it was concluded that MeCD had high affinity for PLLA, and the addition of MeCD increased the amorphous component of PLLA and enhanced the drawability.