Conductivity tensor imaging (CTI) using MRI is an advanced method that can non-invasively measure the electrical properties of living tissues. The contrast of CTI is based on underlying hypothesis about the proportionality between the mobility and diffusivity of ions and water molecules inside tissues. The experimental validation of CTI in both in vitro and in vivo settings is required as a reliable tool to assess tissue conditions. The changes in extracellular space can be indicators for disease progression, such as fibrosis, edema, and cell swelling. In this study, we conducted a phantom imaging experiment to test the feasibility of CTI for measuring the extracellular volume fraction in biological tissue. To mimic tissue conditions with different extracellular volume fractions, four chambers of giant vesicle suspension (GVS) with different vesicle densities were included in the phantom. The reconstructed CTI images of the phantom were compared with the separately-measured conductivity spectra of the four chambers using an impedance analyzer. Moreover, the values of the estimated extracellular volume fraction in each chamber were compared with those measured by a spectrophotometer. As the vesicle density increased, we found that the extracellular volume fraction, extracellular diffusion coefficient, and low-frequency conductivity decreased, while the intracellular diffusion coefficient slightly increased. On the other hand, the high-frequency conductivity could not clearly distinguish the four chambers. The extracellular volume fraction measured by the spectrophotometer and CTI method in each chamber were quite comparable, i.e., (1.00, 0.98 ± 0.01), (0.59, 0.63 ± 0.02), (0.40, 0.40 ± 0.05), and (0.16, 0.18 ± 0.02). The prominent factor influencing the low-frequency conductivity at different GVS densities was the extracellular volume fraction. Further studies are needed to validate the CTI method as a tool to measure the extracellular volume fractions in living tissues with different intracellular and extracellular compartments.