We present a new data compression algorithm, useful for a visualization and a rough analysis of multi-dimensional numerical simulation results with mesh code. The algorithm consists of a classification or a quantization of single or double precision real data at each mesh point, and a subsequent compression by using a conventional compression algorithm. We describe a data compression method in detail, showing this method does work for several typical problems existing in the numerical simulation in astrophysics by counting a compression efficiency. We also investigate a relation of the compression efficiency and simplicity or complexity of the data distribution. When single precision real data on mesh points are compressed by using 8-bit quantization, the compression rate is at least 75% for complex distribution and more than 93% for simple distribution. A source program based on our compression algorithm written in FORTRAN language is now available for interests.