In this paper we propose a novel method for in-hand object recognition. The method is composed of a grasp stabilization controller and two exploratory behaviours to capture the shape and the softness of an object. Grasp stabilization plays an important role in recognizing objects. First, it prevents the object from slipping and facilitates the exploration of the object. Second, reaching a stable and repeatable position adds robustness to the learning algorithm and increases invariance with respect to the way in which the robot grasps the object. The stable poses are estimated using a Gaussian mixture model (GMM). We present experimental results showing that using our method the classifier can successfully distinguish 30 objects.We also compare our method with a benchmark experiment, in which the grasp stabilization is disabled. We show, with statistical significance, that our method outperforms the benchmark method.