Attribute-based encryption(ABE) has been an active research area in cryptography due to its attractive applications. But almost all attribute-based encryption schemes are based on bilinear maps, which leave them vulnerable to quantum cryptanalysis. The latticebased ABE schemes from the Learning with errors(LWE)have appeared, but they are not efficient enough for practical applications. Thus we propose an efficient attributebased encryption based on the Learning with errors over Rings(R-LWE), which is called ABE R-LWE. The security analysis shows that ABE R-LWE scheme is secure in the selective-set model under the R-LWE assumption, whose security can reduce to the hardness of the shortest vector problem in the worst case on ideal lattices. The efficiency analysis indicates that ABE R-LWE is more efficient than previous ABE cryptosystems on lattices. Attribute-based encryption (ABE) has been an active research area in cryptography due to its attractive applications. The lattice based ABE schemes from the Learning with weak (LWE) have appeared, but they are not efficient enough based on the Learning with errors over Rings (R-LWE), which is called ABE R-LWE. The security analysis shows that ABE R-LWE scheme is secure in the selective-set model under the R-LWE assumption, whose security can reduce to the hardness of the shortest vector problem in the worst case on ideal lattices. The efficiency analysis indicates that ABE R- LWE is more efficient than previous ABE cryptosystems on lattices.