Presentation attacks (or spoofing) on finger-vein biometric capture devices are gaining increased attention because of their wider deployment in multiple secure applications. In this work. we propose a novel method for fingervein Presentation Attack Detection (PAD) by exploring the transfer learning ability of Deep Convolutional Neural Network (CNN). To this extent, we have considered the pre-trained Alex-Net architecture and augmented the existing architecture with additional seven layers to improve the reliability and reduce over-fitting problem. We then fine-tune the modified CNN architecture with the fingervein presentation attack samples to make it adaptable to fingervein Presentation Attack Detection (PAD). Extensive experiments are carried out using two different fingervein presentation attack databases with two different fingervein artefact species generated using two different kinds of printers. Obtained results show consistently high performance of the proposed scheme on both databases that further indicate the robustness and efficiency.