An apparatus, configured to estimate quantity of fuel stored in a vehicle, includes: a fuel tank; a fuel quantity measure; a filtering processor; a filter gain setter, configured to set a filter gain; and a vehicle status detector, configured to detect which one of a starting state, a halted state, a state achieved immediately after stoppage of the vehicle, and a traveling state, wherein the filter gain setter sets: a first gain as the filter gain when the vehicle is the starting state; a second gain as the filter gain, which is larger than the first gain, when the vehicle is in the traveling state or the state achieved immediately after stoppage of the vehicle; and a third gain as a filter gain, which is larger than the first gain and smaller than the second gain, when the vehicle is in the halted state.