With the development of computer technology, the requirement of the methods to verify the authenticity, the validity, and the integrity of information is becoming much bigger. For this purpose, many methods have been generated, such as digital signature, digital watermarking, steganography, and so on. Digital signature is a hot topic in cryptography and it plays a very important role in many fields. A normal digital signature allows a signer to generate a signature of the message with his secret key and the generated signature can be verified by anyone with the signer's public key. Chameleon signature is a non-interactive signature based on the well-established hash-and-sign paradigm, in which the receiver cannot convince the third party of the identity of the signer. Designated-verifier signature is a very useful tool for protecting the privacy of the valid verifier. Motivated by above statements, we construct a new chameleon hash scheme and construct a new DVICPS scheme. Our chameleon hash scheme satisfies all the properties of the normal chameleon hash function. In our hash function the owner of a public key does not need to retrieve the associated secret key. We prove that our new chameleon hash scheme satisfies all the attributes defined in [1] and our chameleon hash scheme is secure assuming Weak Computational Diffie-Hellman (WCDH) assumption is difficult. And we show our chameleon hash scheme is secure based on the difficulty of solving WCDHP assumption. Moreover, we use the proposed chameleon hash function to design a designated-verifier ID-based chameleon proxy signature (DVICPS) scheme. Furthermore, we analyze the security of our DVICPS scheme and prove that our DVICPS scheme is secure in the random oracle model. In our signature scheme, only the receiver who owns the corresponding secret key can verify the validity of the signature which efficiently protects the benefit of the verifier. We also prove that our signature scheme is secure in random oracle model. The success probability of forging our DVICPS scheme is equivalent to solving Computational Diffie-Hellman Problem (CDHP). Thus, our DVICPS scheme is secure and efficient.