Threshold secret sharing is concerned with the splitting of a secret into shares and distributing them to some persons without revealing its information. Any ≤ persons possessing the shares have the ability to reconstruct the secret, but any persons less than cannot do the reconstruction. Linear secret sharing scheme is an important branch of secret sharing. The purpose of this paper is to propose a new polynomial based linear ( , ) secret sharing scheme, which is based on Shamir's secret sharing scheme and ElGamal cryptosystem. Firstly, we withdraw some required properties of secret sharing scheme after reviewing the related schemes and ElGamal cryptosystem. The designed scheme provides the properties of security for the secret, recoverability of the secret, privacy of the secret, and cheating detection of the forged shares. It has half computation overhead than the previous linear scheme.