Optical frequency combs generated from microresonators (especially microresonator soliton combs) have been attracting significant attentions because of the potential to be fully chip-scale. Among various promising applications of soliton combs, coherent optical communications and mm/THz wireless communications require low phase noise of the comb modes and low relative phase noise between the comb modes, respectively. Here, we measure the phase noise of a soliton comb, investigating how the thermorefractive noise of a microresonator influences on the phase noise. We observe the quadratic increase of the phase noise of the comb modes, as the comb mode number, counted from the wavelength of a pump cw laser, increases. In addition, we measure the relative phase noise between the comb modes, showing less influence of the phase noise of pump cw lasers by comparing soliton combs generated from pump cw lasers with low and large phase noise.