A power supply apparatus and an operation-mode determining unit and a method thereof are provided. The power supply apparatus includes first and second control units, a switching unit, a power output unit, and an operation-mode determining unit. The first and second control units provide first and second control signals respectively. The switching unit selects to output the first or second control signal according to a switching signal. The power output unit adjusts its output power in accordance with the control signal output from the switching unit. The operation-mode determining unit compares an operation frequency in the power output unit with a reference frequency, and detects an inductor current in the power output unit. The operation-mode determining unit determines the state of a switching signal and outputs it to the switching unit in accordance with the comparison result and the detection result.