We have measured the Seebeck coefficient of a carbon fabric (CAF) using a homemade measurement system for flexible thermoelectric materials to evaluate Seebeck coefficient along the thickness direction. Our equipment consists of a thermocouple (TC) electrode contacted with a resistive heater and another TC electrode attached to a heat sink. A flexible sample is sandwiched with these TC electrodes and pressed by weights. The equipment is set on a weighing machine in order to confirm and hold the pressing force at the contact between the electrodes and the soft sample. Cu and Pb plates were measured as a reference material to calibrate and clarify the accuracy of our measurement system, and its validity was confirmed. The Seebeck coefficient of a single CAF layer ranged 4.3-5.1 µV/K, independent of extra weight. This fact indicates that the weight of heat sink is enough for stable contact at the TC-electrode/CAF interface. It was found that the Seebeck coefficient of layered CAF increases with an increase in the number of layers, which suggests the influence of the air between the CAF layers even though the heavy weight is used.