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Aiming directly at the frequently used digital signature technologies, which are weak to Substitution Attack and Homeostasis Attack, this article performs the hash transformation on messages before signature. Using the method proposed by J. Seberry, a hash round function is constructed, which simultaneously satisfies the characters of balance, high nonlinearity, strict avalanche criterion and realization of software. Moreover, making use of the hash round function, a new hash algorithm named HRFA (Hash Round Function Algorithm) is contrived. On this basis, aiming at the defect that the existing digital signature algorithms are weak to active attack and impersonation attack, using the hash algorithm named HRFA and the self-certified public key method proposed by Girault, a new kind of digital signature algorithm named H-S DSA (Hash Round Function and Self-certified Public Key System Digital Signature Algorithm) is raised and realized. Finally, this article analyzes the H-S DSA from two aspects of security and time-complexity.