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This paper proposes a practical public key encryption scheme which is provable chosen cipher text(CCA) secure based on the gap computational linear Diffie-Hellman assumption in the standard model. This is the first CCA secure scheme based on the gap computational linear Diffie-Hellman assumption. This scheme is efficient and the proof of the security is tight. We also reduce the size of the public key from $n$ to $2\sqrt{n}$ based on the twin gap computational linear Diffie-Hellman assumption. And the time for encryption and decryption is significantly reduced. And we point out that a generalization of the scheme can be constructed similarly based on the gap $k$-computational linear assumption.