In this paper, we present a parallel algorithm for lossless compression. The algorithm is based on the 3D Wavelet Transform (3-D WT). The system under study consists of a parallel implementation of a wavelet compression software running on a cluster of eight nodes linked by a high performance local area network, Myrinet. The parallel implementation is based on the standard Message Passing Interface (MPI). We have used three implementations of the MPI standard: MPI-BIP, MPICH, and LAM. Experimental results are reported based on these three implementations. We provide performance results of this parallel system for the compression video sequences. Some bugs in efficiency for TCP implementation are reported and resolved for this system.