In this paper, we investigate the problem of power control for streaming variable-bit-rate (VBR) videos in a device-to-device (D2D) wireless network. A VBR video traffic model that considers video frame sizes and playout buffers at the mobile users is adopted. A setup with one pair of D2D users (DUs) and one cellular user (CU) is considered and three modes, namely cellular mode, dedicated mode and reuse mode, are employed. Mode selection for the data delivery is determined and the transmit powers of the base station (BS) and device transmitter are optimized with the goal of maximizing the overall transmission rate while VBR video data can be delivered to the CU and DU without causing playout buffer underflows or overflows. A low-complexity algorithm is proposed. Through simulations with VBR video traces over fading channels, we demonstrate that video delivery with mode selection and power control achieves a better performance than just using a single mode throughout the transmission.