The transition in droplet oscillation arising from the Marangoni effect was analyzed by applying the maximum entropy production principle. Entropy production was calculated by taking the volumetric flow of solution as thermodynamic force and the velocity of oscillating droplets as thermodynamic flow. The result of quantitative analysis showed good agreement with the transition point observed experimentally. This result reflects the universality of the maximum entropy production principle for predicting the transition points between different nonequilibrium states.