Angle-dependent magnetoconductance was measured on an individual surface-curved Bi2Te3 single-crystal nanowire fabricated by electrochemical deposition, where the evolution of surface conduction with wire diameters was investigated. It was found that the magnetoconductance of these nanowires in low field regime can be well described by one-dimensional (1D) weak antilocalization (WAL) model, where the dephasing length of the electrons follows T？1/3 dependence but insensitive to the wire diameter. Meanwhile, such a 1D surface WAL was found to be enhanced significantly with the decrease of the wire diameter.