Petroleum reservoirs under primary, secondary or tertiary recovery processes usually experience simultaneous flow of three fluids phases (oil, water and gas). Reports on some mathematical models for calculating three-phase relative permeability are available in the Literature. Nevertheless, many of these models were designed based on certain experimental conditions and reservoir rocks and fluids. Therefore, special care has to be taken when applying them to specific reservoirs. At the laboratory level, three-phase relative permeability can be calculated using experimental unsteady-state or steady state methodologies. This paper proposes an unsteady-state methodology to evaluate three-phase relative permeability using the equipment available at the petrophysical analysis Laboratory of the Instituto Colombiano del Petróleo (ICP) of Ecopetrol S.A. Improvements to the equipment were effected in order to achieve accuracy in the unsteady-state measurement of three-phase relative permeability. The target of improvements was directed toward to the attainment of two objectives:1) the modification of the equipment to obtain more reliable experimental data and 2) the appropriate interpretation of the data obtained. Special attention was given to the differential pressure and uncertainty measurement in the determination of fluid saturation in the rock samples. Three experiments for three-phase relative permeability were conducted using a sample A and reservoir rock from the Colombian Foothills. Fluid tests included the utilization of synthetic brine, mineral oil, reservoir crude oil and nitrogen. Two runs were conducted at the laboratory conditions while one run was conducted at reservoir conditions. Experimental results of these tests were compared using 16 mathematical models of three-phase relative permeability. For the three-phase relative permeability to oil, the best correlations between experimental data and tests using Blunt, Hustad Hasen, and Baker's models were obtained at oil saturations between 40% and 70%.