A hierarchical key management scheme for mobile agents in e-medicine system enables users, such as patients, doctors, nurses and health visitors, to conveniently and securely access a remote hierarchical medical database system via public networks. Efficient hierarchical key management schemes do not require heavy computations even if the hierarchical structure has too many levels and participants. Chen et al. recently developed a hierarchical key management scheme with date-constraint for mobile agents. The key management scheme of Chen et al. is based the Elliptic Curve Cryptosystem and allows each secret key to be partnered with a validity period by using one-way hash chains. However, the scheme of Chen et al. fails to execute correctly, violates authenticated key security, and requires hundreds of hash functional operations. This investigation discusses these limitations, and proposes an efficient date-constraint hierarchical key management scheme for mobile agents in e-medicine system, which provides a fast key validation and expiration check phase to rapidly check whether the secret keys are valid and time-expired or not. The proposed key management scheme not only provides more security properties and rapidly checks the validation of secret keys, but also reduces the computational cost.