We confined electrons in one-dimensional (1D) geometry on a suspended surface of liquid helium within a narrow channel of a structured substrate. A gate electrode, located underneath the channel, creates a parabolic potential well to confine the electrons. The motion of the electrons across the channel is quantized in the potential well. The energy level separation is 64 mK. We measured the electrical conductance as a function of temperature from 0.5 K down to 40 mK. The measured conductance showed a peak at 0.2 K, which confirms the existence of the confinement potential. The origin of the peak is attributed to intersubband transitions in the potential well. The single channel 1D electron system can be realized when the temperature is much lower than 64 mK.