Industrial woven meshes are composed of metal material and are often used in construction, industrial and residential industries. The context of this work is defect detection in industrial fabrics in the quality control process. It is often performed with a manual method and could be quite tedious and time-consuming. We propose here a method to automatically detect defects in micrometric steel meshes using a Convolutional Neural Network. The database used for this work comes from the real problem of anomaly detection on micrometric woven meshes. This detection is performed through supervised classification with Convolutional Neural Network using a VGG19 architecture. To this aim, we propose a pipeline and a strategy to tackle the small amount of data. It includes i) augmenting the database with translation, rotation and symmetry, ii) using pre-trained weights and iii) checking the learning curve behaviour through cross-validation. The proposed method has been evaluated by automatically detecting if metallic fabrics has defects. Obtain results show that, despite the small size of our databases, detection accuracy of 96% was reached.