A water supply apparatus comprising: a pump; a motor configured to rotate the pump; an inverter configured to apply a voltage having a variable frequency to the motor; a check valve disposed at a discharge side of the pump; a discharge-side pressure sensor configured to measure a discharge-side pressure of the pump at a discharge side of the check valve; and a controller (5, 10) configured to perform a feedback control of controlling a rotational speed of the pump through the motor and the inverter based on a measured value of the discharge-side pressure of the pump in order to keep the discharge-side pressure at a predetermined target pressure, characterized in that the controller (5, 10) is configured to store therein a first lower limit value of the rotational speed which is higher than a shutoff rotational speed, and a second lower limit value of the rotational speed which is lower than the shutoff rotational speed, the shutoff rotational speed being a rotational speed required for achieving the target pressure in a shutoff state, and the controller (5, 10) is configured to switch a lower limit of a command value of the rotational speed of the pump from the first lower limit value to the second lower limit value if the command value of the rotational speed of the pump has been not more than the first lower limit value continuously for a predetermined confirmation time, and determine that the pump is in a low-flow-rate state if the command value of the rotational speed of the pump becomes equal to or lower than the shutoff rotational speed within a predetermined detection time. a pump; a motor configured to rotate the pump; an inverter configured to apply a voltage having a variable frequency to the motor; a check valve disposed at a discharge side of the pump; a discharge-side pressure sensor configured to measure a discharge-side pressure of the pump at a discharge side of the check valve; and a controller (5, 10) configured to perform a feedback control of controlling a rotational speed of the pump through the motor and the inverter based on a measured value of the discharge-side pressure of the pump in order to keep the discharge-side pressure at a predetermined target pressure, characterized in that the controller (5, 10) is configured to store therein a first lower limit value of the rotational speed which is higher than a shutoff rotational speed, and a second lower limit value of the rotational speed which is lower than the shutoff rotational speed, the shutoff rotational speed being a rotational speed required for achieving the target pressure in a shutoff state, and the controller (5, 10) is configured to switch a lower limit of a command value of the rotational speed of the pump from the first lower limit value to the second lower limit value if the command value of the rotational speed of the pump has been not more than the first lower limit value continuously for a predetermined confirmation time, and determine that the pump is in a low-flow-rate state if the command value of the rotational speed of the pump becomes equal to or lower than the shutoff rotational speed within a predetermined detection time. switch a lower limit of a command value of the rotational speed of the pump from the first lower limit value to the second lower limit value if the command value of the rotational speed of the pump has been not more than the first lower limit value continuously for a predetermined confirmation time, and determine that the pump is in a low-flow-rate state if the command value of the rotational speed of the pump becomes equal to or lower than the shutoff rotational speed within a predetermined detection time.