In this paper, we present a new algorithm, called MagnitudeCut, for recovering a signal from the phase of its Fourier transform. We casted our recovering problem into a new convex optimization problem, and then solved it by the block coordinate descent algorithm and the interior point algorithm, in which the iteration process consists of matrix vector product and inner product. We used the new method for reconstruction of a set of signal/image. The simulation results reveal that the proposed MagnitudeCut method can reconstruct the original signal with fewer sampling number of the phase information than that of the Greedy algorithm and iterative method under the same reconstruction error. Moreover, our algorithm can also reconstruct the symmetric image from its Fourier phase.