We study the thermodynamic energy cost required for the shortcuts-to-isothermal (ScI) process that can accelerate the isothermal process at a finite time. Our experiment uses a Brownian particle dragged by the harmonic potential between two equilibrium positions with free energy difference. We confirm theoretically and experimentally that the probability distribution functions of work done during these processes are Gaussian, and the dissipated work for ScI transport is inversely proportional to the driving time, indicating that very prompt transition is impossible because of a diverging driving cost.