This is a report of our recent investigation [C.- M. Chen, D. V. Gal'tsov and D. G. Orlov, Phys. Rev. D 75 (2007), 084030; arXiv:hep-th/0701004] on the extremal dilatonic black holes in four dimensional Gauss-Bonnet gravity. We found that a global solution can exist only when the dilaton coupling is less than a critical value which can be determined numerically. Moreover, the black hole horizon is stretched by the Gauss-Bonnet correction and the entropy is twice the value given by Bekenstein-Hawking formula.