The velocity of the inner region of turbulent flow on a smooth bed has complex profile which can not be described with a simple formula. Though there have been a couple of formulas describing the profile, most of them have very complex forms, i.e., with many terms, with integration form, or with implicit forms. It means that it is hard to use them or it is difficult to estimate their parameters. A new single formula that describes the velocity profile of the inner region of the turbulent flow on a smooth bed was proposed. This formula has a form of the traditional log-law multiplied by a damping function. Introducing only one additional parameter, it can describe the whole inner range nicely. It approximates the law-of-the-wall in the vicinity of the bed and approaches to the log-law in the overlap region. The added parameter, damping factor, can be estimated very easily. It is not sensitive to the Reynolds number change and the velocity profile calculated by the formula does not change much due to the change of the parameter.