In this paper, an active control method for visual object exploration and recognition with an unmanned aerial vehicle is presented. This work uses a convolutional neural network for visual object recognition, where input images are obtained with an unmanned aerial vehicle from multiple objects. The object recognition task is an iterative process actively controlled by a saliency map module, which extracts interesting object regions for exploration. The active control allows the unmanned aerial vehicle to autonomously explore better object regions to improve the recognition accuracy. The iterative exploration task stops when the probability from the convolutional neural network exceeds a decision threshold. The active control is validated with offline and real-time experiments for visual exploration and recognition of five objects. Furthermore, passive exploration is also tested for performance comparison. Experiments show that the unmanned aerial vehicle is capable to autonomously explore interesting object regions. Results also show an improvement in recognition accuracy from 88.14% to 95.66% for passive and active exploration, respectively. Overall, this work offers a framework to allow robots to autonomously decide where to move and look next, to improve the performance during a visual object exploration and recognition task.