Machine learning based sub-systems are increasingly becoming part of IoT edge devices, thereby requiring resource-efficient architectures and implementations, especially when subjected to battery-constrained scenarios. The non-exact nature of Convolutional Neural Networks (CNNs) opens the possibility to use approximate computations to reduce their required runtime and energy consumption on resource-constrained IoT edge devices without significantly compromising their classification output. In this paper, we propose a resilience exploration method and a novel approximate accelerator to speed up the execution of the convolutional layer, which is the most time consuming component of CNNs, for IoT edge devices. Trained CNNs with Caffe framework are executed on a System-on-Chip with reconfigurable hardware available, where the approximate accelerator is deployed. CNN applications developed with Caffe can take advantage of our proposed approximate acceleration to execute them on IoT edge devices.