Traditional transformer differential protection generally uses Fourier transform to calculate fundamental component. It cannot identify low percentage interturn faults inside the transformer. And the operating time is usually more than half a cycle affected by the length of data window. What’s more, the protection may operate by mistake when there is an external fault accompanied by CT saturation. In order to solve the above problems, a new criterion for transformer protection based on Hausdorff distance is proposed in this paper. The similarity of current waveforms on both sides of the transformer is compared to distinguish the internal faults from external ones quickly. Theoretical analysis shows that the length of the data window can be selected arbitrarily in new criteria, which is conducive to improving the protection action speed. At the same time, the double setting threshold ensures not only the rapid tripping speed in the case of severe faults, but also the correct operation of protection when an external fault occurs accompanied with CT saturation. Finally, the validity of criteria is verified based on PSCAD/EMTDC. The simulation results show that the criteria can operate quickly and the action time can be as short as 5.5 ms. And the protection can operate in one cycle after fault even if the percentage of interturn fault is only 0.5%. Besides, it has strong anti-CT saturation performance. This work is supported by National Natural Science Foundation of China (No. 51677108) and Science and Technology Project of Guangdong Power Grid Co., Ltd. (No. GDKJQQ20161176).