A near infrared and visible light Fourier transform spectrometer needs to use a multiplied reference laser interfere signal as its sampling signal. Since a phase-locked loop frequency multiplier is not suitable for low frequency non-periodic signals and the traditional digital multiplier method may generate a large error, an improved algorithm based on the traditional digital multiplier method is put forward. The algorithm is simulated and verified. The result shows that when the improved algorithm is used, the non-uniformity error of output waveform is improved from the range of -2% to 1.6% to the range of -0.82% to 0.4%. The non-uniformity error is improved greatly.