In this paper, we report on a single-modulator electro-optic frequency comb whose repetition frequency can be modulated at high speed with a modulation rate of 1 MHz. With spectral broadening in a nonlinear fiber, a comb spectrum spanning 1.25 THz (10 nm, the central wavelength is 1550 nm) with 4800 narrow-linewidth combs separated by 260 MHz is achieved. The optical comb pulse width is compressed to 260 fs by dispersion compensation in a single-mode fiber. Also, the impacts of optical fiber amplification and nonlinear spectral broadening on the comb coherence are studied, and the common-mode phase noise of the comb is suppressed by a feedforward method based on the acousto-optic modulator. The developed electro-optic comb has promising applications for molecular spectroscopy and interferometric ranging.