Efficient data compression algorithms can be slow. The purpose of this work is an attempt of efficient parallelization of compression algorithm for execution on graphics processing units. Since graphics processing units contain an efficient parallel computing unit, it is reasonable to expect speedup from such parallelization of the algorithm. This work contains an overview of deflate algorithm and its existing parallel implementations intended for graphics processing units. We sequentially implemented the algorithm and parallelized it in two different ways using OpenCL framework. The implementations were tested on a corpus of files, intended for testing of compression algorithms. We compared the results with existing sequential and parallel implementations.