A heating resistor type flow rate measuring apparatus comprising: a first heating resistor arranged in a passage; a support member for supporting said first heating resistor comprising lead conductors; a second heating resistor fixed by welding to said support member; a temperature measuring resistor fixed by welding to said support member interposed between said first heating resistor and said second heating resistor; control means for controlling heat generation by said second heating resistor such that temperatures detected by said temperature measuring resistor fall into a predetermined temperature range inclusive of temperatures of said first heating resistor; characterized by means for determining a flow rate of fluid flowing in said passage based on the temperatures of said first and second heating resistors (1, 6) and a temperature detected by said temperature measuring resistor, wherein the flow rate determination means are configured to: set initial values of a fluid temperature and fluid flow rate; calculate a thermal conductivity at the surface of the temperature measuring resistor and at the lead conductor surfaces; determine a resistance value of the first heating resistor, a resistance value of the second heating resistor and a resistance value of the temperature measuring resistor; calculate a temperature of the first heating resistor, a temperature of the second heating resistor and a temperature of the temperature measuring resistor; calculate temperatures of the lead conductors; control through feedback control a supply current of the first heating resistor and a supply current of the second heating resistor such that the temperatures of the first and second heating resistor reach target temperatures; determine an update value of the fluid temperature; determine an update value of the fluid flow rate; set the update value of the fluid temperature as initial fluid temperature value and the update value of the fluid flow rate as initial fluid flow value if a change width of the flow rate is larger than a predetermined value; and repeat the above steps until the change width becomes less than the predetermined value. a first heating resistor arranged in a passage; a support member for supporting said first heating resistor comprising lead conductors; a second heating resistor fixed by welding to said support member; a temperature measuring resistor fixed by welding to said support member interposed between said first heating resistor and said second heating resistor; control means for controlling heat generation by said second heating resistor such that temperatures detected by said temperature measuring resistor fall into a predetermined temperature range inclusive of temperatures of said first heating resistor; characterized by means for determining a flow rate of fluid flowing in said passage based on the temperatures of said first and second heating resistors (1, 6) and a temperature detected by said temperature measuring resistor, wherein the flow rate determination means are configured to: set initial values of a fluid temperature and fluid flow rate; calculate a thermal conductivity at the surface of the temperature measuring resistor and at the lead conductor surfaces; determine a resistance value of the first heating resistor, a resistance value of the second heating resistor and a resistance value of the temperature measuring resistor; calculate a temperature of the first heating resistor, a temperature of the second heating resistor and a temperature of the temperature measuring resistor; calculate temperatures of the lead conductors; control through feedback control a supply current of the first heating resistor and a supply current of the second heating resistor such that the temperatures of the first and second heating resistor reach target temperatures; determine an update value of the fluid temperature; determine an update value of the fluid flow rate; set the update value of the fluid temperature as initial fluid temperature value and the update value of the fluid flow rate as initial fluid flow value if a change width of the flow rate is larger than a predetermined value; and repeat the above steps until the change width becomes less than the predetermined value. set initial values of a fluid temperature and fluid flow rate; calculate a thermal conductivity at the surface of the temperature measuring resistor and at the lead conductor surfaces; determine a resistance value of the first heating resistor, a resistance value of the second heating resistor and a resistance value of the temperature measuring resistor; calculate a temperature of the first heating resistor, a temperature of the second heating resistor and a temperature of the temperature measuring resistor; calculate temperatures of the lead conductors; control through feedback control a supply current of the first heating resistor and a supply current of the second heating resistor such that the temperatures of the first and second heating resistor reach target temperatures; determine an update value of the fluid temperature; determine an update value of the fluid flow rate; set the update value of the fluid temperature as initial fluid temperature value and the update value of the fluid flow rate as initial fluid flow value if a change width of the flow rate is larger than a predetermined value; and repeat the above steps until the change width becomes less than the predetermined value.