Actin filaments play critical roles in various cellular functions such as migration, division and shape control. In these activities, microscopic mechanical stretching, twisting and bending cause structural changes at the molecular level in single actin filaments. The actin filaments have a double helical structure consisting of globular actin molecules, that induces coupling behaviors between stretching and twisting of the filaments. Thus, tension acting on the filaments modulates the twisting dynamics of filaments, and may change affinity of regulatory actin-binding proteins which depend on the twisting behaviors of actin filaments. For better understanding of actin dynamics containing the tension and the actin-binding proteins, it is important to evaluate the extension-torsion coupling behaviors of actin filaments. This study evaluates the extension-torsion stiffness of single actin filament using molecular dynamics simulations. To evaluate the extension-torsion coupling behaviors, stretching and twisting Brownian motions of the filament were analyzed. The results demonstrated that the longitudinal and twisting motions of the filament exhibit a correlation. From the correlation, we evaluated the extension-torsion coupling stiffness of the filament based on statistical-mechanical theory.