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Most of the hash functions using iterative constructions, are inefficient for bulk hashing of documents with high similarity. In this paper, we present a new approach to construct a cryptographic hash function called Pair Chaining & Modular Arithmetic Combining Incremental Hash Function (PCIHF). PCIHF has some attractive properties, which are incrementality and parallelizability. The security of PCIHF has also been analyzed comprehensively. Finally, we show that PCIHF is not only universal one-way but also collision-free.