Interleaving technology plays an important role in most digital communication systems. The data stream is sent to an interleaver that rearranges the data in order to cope with burst errors and improve the reliability of data transmission. Considering the reconstruction of convolutional interleaver in a non-cooperative context, and an algorithm based on the first order cumulant of the data stream is proposed in this paper. The period of the data stream is detected according to the cumulants of the Attached Sync Markers (ASM) and code words. The depth and width of the convolutional interleaver are estimated according to the distributions of the ASMs. The simulation results show that the proposed method provides an optimal performance in the noisy environment and has less computational load than the Gaussian elimination algorithm.