Image inpainting is to restore a damaged image with missing information – a fundamental problem and a hot research area in image processing. Many approaches, both geometry oriented and texture oriented, have been proposed on inpainting such as total variation (TV), Criminisi algorithm, etc. However, these approaches suffer from either limitations such as only suitable for small areas (cracks), staircase effect (discontinuity), or inefficient (time-consuming) to search the best matched patch (for filling-in). In this paper we propose a novel approach based on partial differential equation (PDE) and isophotes direction, named as Isophotes-TV-H<sup>-1</sup>. A corrupted image is first decomposed into two parts: the cartoon (smooth parts and edges of the image) and the texture. The cartoon part is inpainted through Isophotes- TV-H<sup>-1</sup> while the texture part is done by an enhanced Criminisi algorithm which reduces the searching time for match and gives more reasonable match patches. The results of experiments on several images have demonstrated that, compared to existing methods, the proposed solution can recover the texture (of the damaged region) better, suppress error propagation and solve the problem of intensity discontinuity.