Different from the above prior works focusing on the ML strategy or structure design for improving the communication performance, this letter proposes to employ the emerging communication technique, namely the device-to-device (D2D) communications (see, e.g., [10, 11]), to relieve the "straggler's dilemma" issue for improving the performance of distributed ML-model training. Recently, the D2D communications have been recognized as one key technique in fifth-generation (5G) and beyond cellular networks, in which wireless devices in close proximity can directly communicate with each other without going through cellular infrastructures such as base stations (BSs). Motivated by this, we propose a new D2D-enabled data sharing design for mobile edge learning, which allows edge devices to share their data samples over D2D communication links. By properly controlling the amounts of data samples exchanged, this design can not only adjust the computation loads at devices for enhancing the training speed, but also reshape the data distribution (if data samples at edge devices are non-IID) for enhancing the training accuracy. In particular, we aim to minimize the total delay for the ML-model training under fixed numbers of local and global iterations (for training), by optimizing the radio resource allocation for both D2D data sharing and distributed model training.