A voltage regulator and a power supply are provided. The voltage regulator includes an operational amplifier and an offset voltage control module. The operational amplifier includes an input terminal and an output terminal, and is configured to generate an output voltage to be output from the output terminal based on a reference voltage received from the input terminal. The offset voltage control module includes one stage of regulation branch or more stages of regulation branches connected in parallel, and is configured to control an offset voltage of the operational amplifier based on selection of the regulation branch to regulate the output voltage. Since sine each stage of regulation branch in the offset voltage control module is based on a transistor structure, as compared with the voltage dividing resistor in the related art, the transistor has lower power consumption, and thus power consumption of the voltage regulator is lowered.