We present a high-speed swept-source optical coherence tomography (SS-OCT) imaging system using an electrically-pumped, micro-electromechanical-system (MEMS) tunable HCG-VCSEL operating at the 1060 nm wavelength regime. Comparing to existing MEMS VCSEL light sources for SS-OCT, a movable high-contrast grating (HCG) is used as the top mirror of the laser cavity, replacing the conventional distributed Bragg reflector mirror design. By applying a reverse bias voltage, the HCG mirror actuates downward toward the VCSEL cavity, changing the effective cavity length and resulting in wavelength tuning responses. The developed SS-OCT system allows an A-scan rate of 250 kHz, a detection sensitivity of 98 dB, and an axial imaging resolution of 22 µm (full-width at half-maximum (FWHM), in air). The A-scan rate can be further improved to 500 kHz if both the backward (long to short wavelength) and forward laser sweep are used. In the experimental setup, a dual-channel acquisition scheme was utilized to provide calibration of the OCT signal with a separate calibration interferometer. Volumetric imaging of the human fingernail/nail fold junction in vivo shows the feasibility of providing high-speed imaging of the tissue architectures. The MEMS tunable HCG-VCSEL light source can provide high-speed OCT imaging with a more compact light source footprint and potentially a lower cost.