A multi-phase buck converter has a digital compensator to select a set of compensation coefficients depending on the operating phase number of the multi-phase buck converter, or including different compensators for each operation phase number to improve the loop gain bandwidth, transient response and stability of the multi-phase buck converter. The multi-phase buck converter operates with more phase circuits for higher loading and operates with fewer phase circuits for lower loading. The compensation varies with the number of the operated phase circuits so to be adaptive to the operation condition with an optimized control-to-output voltage transfer function.