A graded index porous optical fiber incorporating an air-hole array featuring variable air-hole diameters and inter-hole separations is proposed, fabricated, and characterized in a view of the fiber potential applications in low-loss, low-dispersion terahertz guidance. The proposed fiber features simultaneously low modal and intermodal dispersions, as well as low loss in the terahertz spectral range. We experimentally demonstrate that graded index porous fibers exhibit smaller pulse distortion, larger bandwidth, and higher excitation efficiency when compared to fibers with uniform porosity.