We propose a multi-wavelength digital holography based on Kramers-Kronig (KK) relations, introducing a unified angle-multiplexing multi-wavelength KK model to overcome the accuracy and resolution limitations of angle-multiplexing techniques. By linking the real and imaginary parts of the multi-wavelength complex function via the KK relation, the method captures object light waves with the full effective bandwidth from a single interferogram and reference wave intensity. This method greatly improves spectral utilization and measurement accuracy in multi-wavelength interference. We use a three-wavelength multiplexing system to measure the topography of multi-step samples. The results show that our method expands the spectral range more than twice, reduces errors by 39.3%, and improves the peak signal-to-noise ratio and structural similarity index nearly three times compared to the traditional Fourier transform (FT) method. It offers a new, to the best of our knowledge, approach for high-precision multi-wavelength dynamic measurement and has the potential to overcome the limitations of multiplexing technology.