Structured clouds and ground building background suppression are difficult problems for dim and small target detection technique. In this paper, the dim and small target background suppression method based on combined curvelet transform with modified non-local means filter was presented to solve the problem. And local gradient statistics is introduced to boost ability of method which suppresses false by background structure. The innovation was that the curvelet transform was adopted to decompose the input infrared image, which extracts multi-scale and directional detail features of the image. Moreover non-local means filter improved by local gradient characteristic was introduced to suppress background details and enhance target information for suppression background. Compared with two-dimensional least mean square (TDLMS) and modified partial differential equation (MPDE) methods, through visual quality and value index, several groups of experimental results demonstrate that the presented method can suppress complicated background in dim and small target image effectively.