The optical and electrical characteristics of a graphene oxide solution (GS) with different graphene oxide (GO) concentrations in de-ionized water are investigated via the electrochemical impedance spectroscopy (EIS) method. The measurement results produced by the EIS for the GS are represented with both Bode and Nyquist plots in a frequency range from 1 kHz to 10 MHz. Using these results, we develop an equivalent circuit model as a function of the GO concentration, representing the GS as a mixed circuit of two-dimensional (2D) GO dispersed in parallel in de-ionized (DI) water. The underlying physics of the current-flowing behavior in the GS are explained and interpreted using empirical circuit models; the circuit model also shows that highly resistive GO becomes conductive in GS form in the DI water. The findings in this work should draw new attention toward GSes and related applications, including functional composite materials, catalysts, and filter membranes.