The 3rd Generation Partnership Project (3GPP) has recently developed device-to-device (D2D) communication to cope with the explosively increasing mobile data traffic. The D2D communication uses sidelink that is based on the single-carrier frequency-division multiple access scheme because of its low peak-to-average power ratio. In addition, the demodulation reference signal is designed to support multiple input multiple output. In this paper, we propose a DFT-based channel estimation scheme for sidelink in D2D communication. The proposed scheme uses the two-dimensional minimum mean square error interpolation scheme for a user moving at a high speed. We performed a system level simulation based on 20-MHz bandwidth of the 3GPP LTE-Advanced system. Simulation results show that the proposed channel estimation scheme has improved signal-to-interference-plus-noise ratio, throughput, and spectral efficiency as compared with a conventional scheme.