An audio signal level compressor is presented, which is based on the approximation algorithm using an interpolating polynomial. To implement a compression characteristic in a digital audio system, a power calculation with fractional numbers is required and it is difficult to be performed directly in digital circuits. We introduce a polynomial expression to approximate the power operation, then the gain calculation is easily performed with a number of additions, multiplications and a division. Newton's interpolation formula is used to calculate the compression characteristics in a very short time and the obtained compression characteristics are very close to the ideal ones.