Finger-vein recognition, a new and advanced biometrics recognition method, is attracting the attention of researchers because of its advantages such as high recognition performance and lesser likelihood of theft and inaccuracies occurring on account of skin condition defects. However, as reported by previous researchers, it is possible to attack a finger-vein recognition system by using presentation attack (fake) finger-vein images. As a result, spoof detection, named as presentation attack detection (PAD), is necessary in such recognition systems. Previous attempts to establish PAD methods primarily focused on designing feature extractors by hand (handcrafted feature extractor) based on the observations of the researchers about the difference between real (live) and presentation attack finger-vein images. Therefore, the detection performance was limited. Recently, the deep learning framework has been successfully applied in computer vision and delivered superior results compared to traditional handcrafted methods on various computer vision applications such as image-based face recognition, gender recognition and image classification. In this paper, we propose a PAD method for near-infrared (NIR) camera-based finger-vein recognition system using convolutional neural network (CNN) to enhance the detection ability of previous handcrafted methods. Using the CNN method, we can derive a more suitable feature extractor for PAD than the other handcrafted methods using a training procedure. We further process the extracted image features to enhance the presentation attack finger-vein image detection ability of the CNN method using principal component analysis method (PCA) for dimensionality reduction of feature space and support vector machine (SVM) for classification. Through extensive experimental results, we confirm that our proposed method is adequate for presentation attack finger-vein image detection and it can deliver superior detection results compared to CNN-based methods and other previous handcrafted methods.