Public verifiability in signcryption achieves public verification of signature by a trustable third party; it ensures the reliability and secure parity of signcryption scheme. In the paper, we analyzed the public verification algorithm in signcryption and presented signcryption scheme without verifiability based on discrete logarithm problem as a comparison. Signcryption without verifiability satisfies the basic requirements of authenticated encryption; it can achieve secret message transmission and identity authentication in a single protocol. But the signcryption sender can cheat in the protocol with forged information for lack of supervision by public verification. Then we presented an improved signcryption scheme with public verifiability, in the scheme signcryption message is generated with private key of message sender and other public parameters, any trustable third party can verify the signcryption without disclosing private key or secret parameters. Besides, the attack on the signcryption and secret parameters via public verification data is computationally infeasible. The scheme reinforces the security and reliability of signcryption and effectively improves its efficiency for engineering application.