By using local and global image information, a novel active contour method based on the p-Laplace equation for image segmentation is proposed in this paper. The force term in the evolution equation incorporates global, local and edge information of the image. The global and local terms drag the contour towards object boundaries precisely and take care of the contour movement when it is away from the object. Meanwhile, the integration of edge stopping function in this force term ensures the stoppage of contour at object boundaries to avoid boundary leakage problem. The variable exponent p-Laplace energy is used for smoothness of the level set to detect the exact object boundaries in the presence of complex topological changes and deep depression. Finally, the adaptive force and p-Laplace energy term are jointly integrated into a level set by using a simple finite difference scheme to build the final evolution equation for the method. The proposed method has strong capability to accurately segment the images having noise, intensity inhomogeneity, and complex object boundaries. Moreover, the proposed method overcomes the problem arise from contour initialization as the evolution of contour is independent of the initialization of level set function. Experimental results on synthetic, real and medical images along with two publicly available databases validate the robustness and effectiveness of the proposed method.