Focusing on the low accuracy and long detection time of arc detection in engineering drawing vectorization, a fast arc detection algorithm based on tangent lines matching was proposed. Firstly, tangent lines on the circle outer boundary were detected from eight directions (0, π/4, π/2, …, 7π/4) and were added in tangent lines set. Secondly, the tangent lines in the set were paired up, and the center and radius of circles were estimated to obtain circle candidate set. Finally, tracing detection was performed for every candidate circle after merging data of circle candidate set, and every candidate circle was ascertained as a circle or an arc. The paring process was executed during the tangent lines searching, and the number of pairing was effectively reduced by removing the relative tangent lines of the identified candidate circle. In the contrast experiments with RANdom SAmple Consensus (RANSAC) algorithm and Effective Voting Method (EVM), the proposed method reached average detection accuracy of 97.250%, and the average detection time was 12.290 s, which were better than those of the comparison methods. The experimental results illustrate that the proposed method can effectively detect the arc which length is greater than 1/8 circumference in low noise image, improve the accuracy of detection and shorten the detection time.