Gauss coefficients of Mercury's internal/external magnetic field with high time resolution are essential to delineate electrical properties within Mercury. Although the time-averaged structure of Mercury's magnetic field has been studied so far, its time variation has been less studied using the observed data directly. Here we determined the annual and semi-annual variations of Mercury's external magnetic field in Mercury Year as the characteristic periods that contribute to electromagnetic (EM) induction by converting the magnetopause-crossing data of MESSENGER into the subsolar distance. We obtained the time series of Mercury's internal Gauss coefficients by spherical harmonic analyses of MESSENGER's vector magnetic data using a series of constrained inversions. In the inversions, we used KT14 model as a function of the subsolar distance to estimate the external magnetic field at desired moments. Finally, we estimated the core radius of Mercury as 2011 ± 180 km from the inductive response of the annual variation.