This paper focuses on k-reach query processing based on graph compression and proposes a k-reach query preserving graph compression algorithm k-RPC and a query processing algorithm which is able to query on the compressed graph without decompression. k-RPC algorithm is optimal among all the compression algorithms based on equivalent class which supports k-reach query. Considering k-RPC is based on a strict equivalent relation, this study further produces a linear approximate graph compression algorithm k-GRPC. k-GRPC first removes some edges from the input graph, then utilizes k-RPC to acquire better compression ratio. Novel linear query processing algorithms which are able to answer k-reach query on the compressed graph without decompression are introduced. Experiments on real datasets demonstrate that the compression ratios of these two compression algorithms can reach to 45% for sparse graphs and 75%, 67% for dense graphs. Comparing with the query processing on original graphs, the query performance on compressed graphs is better and for sparse graphs, it can be 2.5 times better.