Electronic prescription is increasingly popular in our society, particularly in technologically advanced countries. Due to strict legal requirements and privacy regulations, authorization and data confidentiality are two important features in electronic prescription system. By combining signature and encryption functions, signcryption is an efficient cryptographic primitive that can be used to provide these two features. While signcryption is a fairly established research area, most signcryption schemes proposed recently have several limitations (e.g., high communication costs, limited bandwidth, and insecurity), and designing secure and practical signcryption schemes remains challenging. In this paper, we propose an improved certificateless proxy signcryption (CLPSC) scheme, based on elliptic curve cryptography (ECC). We also demonstrate that the proposed CLPSC scheme is secure in the random oracle model and evaluate its performance with related schemes. The security and performance evaluations show that the proposed CLPSC scheme can potentially be implemented on resource-constrained low-computing mobile devices in an electronic prescription system.