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While the original public-key encryption with keyword search scheme (PEKS) has been pointed out to be insecure against off-line keyword-guessing attacks, some public-key encryption with designated tester schemes (dPEKS) proposed recently also encounter the same attacks. Rhee et al. proposed a dPEKS which is intended to prevent the off-line keyword-guessing attacks. However, we find that the off-line keyword-guessing attacks are still working in the test phase when some malicious servers exist. Hence, we add a random parameter into the test phase of Rhee et al.'s scheme to get a more secure and improved dPEKS scheme so as to prevent from keyword-guessing attacks and to benefit the advantages of dPEKS as well.