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This paper presents a compression algorithm for dynamic data, the size of which keeps on increasing rapidly. It is a memory efficient data compression technique comprising of a block approach that keeps the data in compressed form as long as possible and enables the data to be appended to the already compressed text. The algorithm requires only a minimal decompression for supporting update of data using a little preprocessing which reduces the unnecessary time spent in compression-decompression to support update by the algorithms deigned till now to a minimum. Further, the text document can be modified as required without decompressing and again compressing the whole document. The paper also presents the design of the required data structures for our algorithm with performance results.