Images with intensity inhomogeneity and blurred boundaries are common in image segmentation tasks, which inevitably result in many difficulties in accurate image segmentation. Massive active contour models (ACMs) have been proposed to solve the problems of intensity inhomogeneity or blurred boundaries respectively. However, there is almost no way to effectively solve the above two problems at the same time, and they are sensitive to the initial contour and noise, or their segmentation speed is relatively slow. In this paper, we propose an active contour model (ACM) based on adaptively variable exponent combining Legendre polynomial (LP) for image segmentation. First, the Legendre polynomial intensity (LPI) is defined, which employs a linear combination of Legendre basis functions for region intensity approximation. Second, an adaptively LPI term is defined, which adopts an adaptively variable exponent function as an acceleration term to drive the curve to quickly evolve to the object boundaries. Third, the distance regularization term is introduced into the active contour as a regularization term to eliminate the need for reinitialization and restrict the behavior of level set function (LSF). Experimental results show that our method offers robustness to gray unevenness, noise and initial curve placement, and adaptability to low contrast and blurred boundaries and outperforms other state-of-the-art algorithms.