In this paper, a novel method is proposed for curve detection in images using a feature-related searching control model. It is composed of three parts: 1) prediction; 2) searching; and 3) updating. First, curve related features are modeled to a three order array. Then, equations of the prediction, searching, and curve parameter updating are deduced. Third, an optimal model for curve parameter estimation during iterations is given. Based on the proposed model, a curve detection algorithm is designed. Experiments on thousands of images demonstrate the effectiveness and advantages of the proposed method. Comparison experiments with state-of-the-art methods show that the proposed method outperforms the existing methods on most indexes. Our method can describe the contents of original images more completely with fewer curves. The contour evaluation framework and the Berkeley segmentation dataset are used to evaluate the performances of different curve detection methods. The proposed method can also detect curves in the order relates to their importance, which has been validated in experiments.