Single-phase Auto-reclosing (SPAR) is widely used on EHV/UHV transmission lines to improve power system reliability. However, reclosing on to a permanent fault can adversely affect the system stability and damage generators and other equipment connected to the line. To solve this problem, a new algorithm for improving the single-phase adaptive autoreclosure is presented in this paper. Firstly, primary and secondary arc models are introduced, then a series of simulations are carried out based on the arc models. By analyzing the simulation results, a new method to discriminate between transient faults and permanent faults is proposed. Since fault arcs are associated with transient faults, and the frequent re-ignitions of the secondary arc cause distortions in the line voltage, a reliable single-phase autoreclosure can be achieved by measuring the distortion in the line voltage waveform. In order to improve the distortion detection, Multi-resolution Morphological Gradient (MMG) has been adopted. Finally, numerous simulation results show that the algorithm proposed in this paper can be used as an effective tool for realizing the SPAR.