Directionality of image plays a very important role in human visual system and it is important prior information of image.In this paper we propose a weighted directional total variation model to reconstruct image from its finite number of noisy compressive samples.A novel self-adaption,texture preservation method is designed to select the weight.Inspired by majorization-minimization scheme,we develop an efficient algorithm to seek the optimal solution of the proposed model by minimizing a sequence of quadratic surrogate penalties.The numerical examples are performed to compare its performance with four state-of-the-art algorithms.Experimental results clearly show that our method has better reconstruction accuracy on texture images than the existing scheme.