In this paper the concept of annular thermoelectric cooler (ATEC) has been introduced. An exoreversible thermodynamic model of the annular thermoelectric cooler considering Thomson effect in conjunction with Peltier, Joule and Fourier heat conduction has been investigated using exergy analysis. New expressions for optimum current at the maximum energy/exergy efficiency, maximum cooling power conditions and dimensionless irreversibilities in the ATEC are derived. The modified expression for figure of merit of a thermoelectric cooler considering the Thomson effect has also been obtained. The results show that the cooling power, energy and exergy efficiency of the ATEC is lower than the flat plate thermoelectric cooler. The effects of annular shape parameter (S-r = r(2)/r(1)), dimensionless temperature ratio (0 = T-h/T-c) and the electrical contact resistances on cooling power, energylexergy efficiency of an ATEC have been studied. It has also been proved that because of the influence of Thomson effect, the cooling power and energy/exergy efficiency of the ATEC is increased. This study will help in the designing of the actual annular thermoelectric cooling systems. (C) 2015 Elsevier Ltd. All rights reserved.