Phelix is a candidate algorithm for the ESTREAM stream cipher project. An algorithm was presented to solve a system of differential equations based on single-bit fault on XY=Z in this paper. Then a bit-oriented differential fault analysis of Phelix based on the algorithm was shown. Theoretically, the 256-bit working key can be obtained by using 652 bit-faults, with the computational complexity of O(220). The result shows that the stream cipher Phelix is vulnerable to differential fault analysis.