Based on Shamir's threshold scheme and elliptic curve, a new secret sharing scheme for general access structure is proposed. It is able to prevent adversaries from getting the secret and efficiently guard against cheating among participants. Each participant's secret is selected by participant himself and the dealer need not deliver any secret information to each participant. The secret does not need to be changed when the shared secret is renewed, the access structure is altered, and participants are added or deleted. The scheme is characterized by excellent security as well as high efficiency because of no secret communication required in the secret distribution phase.