Compressive imaging presents the challenge of reconstructing an image accurately from its under-sampling measurements. The total variation model, used as the regularization for imaging reconstruction, ignores structure direction, which tends to result in over-smoothing of homogenous regions and staircase artifacts in textured regions. This paper proposes to solve this problem using a compressive reconstruction method with adaptive directional total variation (DTV) based on the structure orientation field (SOF). This approach builds the estimation model of the structure tensor upon the Huber norm as the penalty term, reducing the degradation influence and reaching a quick solution using the primal-dual algorithm. The method then uses the structure tensor to describe the SOF and to establish compressive reconstruction in which the SOF restricts the DTV regularization. Finally, by analyzing the structure of the objective function, this approach adopts the linearized alternating direction method of multipliers to address the challenges presented by the reconstruction model. The experimental results show that the proposed method requires fewer iterations and demonstrates better reconstruction performance than existing methods, as indicated by examining texture details for visual fidelity and quality as measured through other objective criteria.