In this paper,we present the first ciphertext-policy attribute-based encryption(CP-ABE)scheme for polynomial-size general circuits based on bilinear maps which is more suitable for practical use and more efficient than multilinear maps. Our scheme uses a top-down secret sharing and FANOUT gate to resist the “backtracking attack” which is the main barrier expending access tree to general circuit. In the standard model,selective security of our scheme is proved. Comparing with current scheme for general circuits from bilinear maps,our work is more efficient. In this paper, we present the first ciphertext-policy attribute-based encryption (CP-ABE) scheme for polynomial-size general circuits based on bilinear maps which is more suitable for practical use and more efficient than multilinear maps. Our scheme uses a top -down secret sharing and FANOUT gate to resist the “backtracking attack ” which is the main barrier expending access tree to general circuit. In the standard model, selective security of our scheme is proved. Comparing with current scheme for general circuits from bilinear maps, our work is more efficient.