An apparatus for supplying fuels of a bi-fuel engine, the apparatus comprising: a fuel supply flow passage that is connected to an engine; a liquefied gas fuel supply flow passage that is connected to the fuel supply flow passage and allows a liquefied gas fuel to be supplied from a liquefied gas fuel tank to the fuel supply flow passage, a liquid fuel supply flow passage that is connected to the fuel supply flow passage and allows a liquid fuel to be supplied from a liquid fuel tank to the fuel supply flow passage; a fuel selection valve that allows the liquefied gas fuel supply flow passage or the liquid fuel supply flow passage to be selectively open; a first chamber which is connected to the liquid fuel supply flow passage and in which the liquid fuel supplied to the liquid fuel supply flow passage is stored; and a pressurizing unit that operates so that a volume of an internal space of the first chamber is reduced and that pressurizes the liquid fuel stored in the first chamber, characterized in that the pressurizing unit comprises a first piston that is disposed to be able to make a reciprocal motion within the first chamber and pressurizes the liquid fuel stored in the first chamber as the first piston is moved in a first direction of reciprocal motion directions, and a second piston that is disposed to be able to make a reciprocal motion within a second chamber; is connected by a piston rod to the first piston and makes a reciprocal motion together with the first piston as one body, and in that the second piston is moved in the first direction or makes a reciprocal motion due to a pressure of the liquefied gas fuel supplied from the liquefied gas fuel supply flow passage into the second chamber. a fuel supply flow passage that is connected to an engine; a liquefied gas fuel supply flow passage that is connected to the fuel supply flow passage and allows a liquefied gas fuel to be supplied from a liquefied gas fuel tank to the fuel supply flow passage, a liquid fuel supply flow passage that is connected to the fuel supply flow passage and allows a liquid fuel to be supplied from a liquid fuel tank to the fuel supply flow passage; a fuel selection valve that allows the liquefied gas fuel supply flow passage or the liquid fuel supply flow passage to be selectively open; a first chamber which is connected to the liquid fuel supply flow passage and in which the liquid fuel supplied to the liquid fuel supply flow passage is stored; and a pressurizing unit that operates so that a volume of an internal space of the first chamber is reduced and that pressurizes the liquid fuel stored in the first chamber, characterized in that the pressurizing unit comprises a first piston that is disposed to be able to make a reciprocal motion within the first chamber and pressurizes the liquid fuel stored in the first chamber as the first piston is moved in a first direction of reciprocal motion directions, and a second piston that is disposed to be able to make a reciprocal motion within a second chamber; is connected by a piston rod to the first piston and makes a reciprocal motion together with the first piston as one body, and in that the second piston is moved in the first direction or makes a reciprocal motion due to a pressure of the liquefied gas fuel supplied from the liquefied gas fuel supply flow passage into the second chamber.