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We present PEP, which is a new construction of a tweakable strong pseudo-random permutation. PEP uses a hash-encrypt-hash approach which has been recently used in the construction of HCTR. This approach is different from the encrypt-mask-encrypt approach of constructions such as CMC, EME and EME*. The general hash-encrypt-hash approach was earlier used by Naor-Reingold to provide a generic construction technique for an SPRP (but not a tweakable SPRP). PEP can be seen as the development of the Naor-Reingold approach into a fully specified mode of operation with a concrete security reduction for a tweakable strong pseudo-random permutation. HCTR is also based on the Naor-Reingold approach but its security bound is weaker than PEP. Compared to previous known constructions, PEP is the only known construction of tweakable SPRP which uses a single key, is efficiently parallelizable and can handle an arbitrary number of blocks.