A method to control an internal combustion engine provided with a mass flow sensor (9; 39) and with an exhaust system for the exhaust gases of a motor vehicle having an exhaust duct and an exhaust gas after-treatment system comprising at least one catalytic converter (15, 17) arranged along the exhaust duct; a burner, which is suited to introduce exhaust gases into the exhaust duct so as to speed up the heating of said at least one catalytic converter (15, 17), wherein inside the burner there is defined a combustion chamber, which receives fuel from an injector, which is designed to inject fuel into the combustion chamber, and fresh air through an air feeding device, which is provided with a pumping device feeding air, and with a shut-off valve arranged upstream of the burner; the method comprises the following steps: calculating the thermal power (P OBJ) needed to reach the nominal operating temperature of said at least one catalytic converter (15, 17); determining the objective air flow rate (ṁ A_OBJ) to be fed to the burner in order to obtain said thermal power (P OBJ) needed to reach the nominal operating temperature of said at least one catalytic converter (15, 17); determining the nominal number (N NOM) of revolutions with which to operate the pumping device by means of a map depending on the objective air flow rate (ṁ A_OBJ), on the ambient pressure (P ATM), on the ambient temperature (T ATM) and on the pressure (P A) of the air flowing into the burner; determining a closed-loop contribution (N CL) of the number of revolutions with which to operate the pumping device by means of a PID controller, which tries to zero a difference between the objective air flow rate (ṁ A_OBJ) and the air flow rate (ṁ A) determined through the mass flow sensor (9; 39); determining a further contribution (N ADAT) of the number of revolutions with which to operate the pumping device depending on the integral action of the PID controller under stationary conditions; and determining the actual number of revolutions with which to operate the pumping device by means of the sum of the nominal number (N NOM) of revolutions, of the closed-loop contribution (N CL) of the number of revolutions with which to operate the pumping device and of the further contribution (N ADAT) of the number of revolutions with which to operate the pumping device. calculating the thermal power (P OBJ) needed to reach the nominal operating temperature of said at least one catalytic converter (15, 17); determining the objective air flow rate (ṁ A_OBJ) to be fed to the burner in order to obtain said thermal power (P OBJ) needed to reach the nominal operating temperature of said at least one catalytic converter (15, 17); determining the nominal number (N NOM) of revolutions with which to operate the pumping device by means of a map depending on the objective air flow rate (ṁ A_OBJ), on the ambient pressure (P ATM), on the ambient temperature (T ATM) and on the pressure (P A) of the air flowing into the burner; determining a closed-loop contribution (N CL) of the number of revolutions with which to operate the pumping device by means of a PID controller, which tries to zero a difference between the objective air flow rate (ṁ A_OBJ) and the air flow rate (ṁ A) determined through the mass flow sensor (9; 39); determining a further contribution (N ADAT) of the number of revolutions with which to operate the pumping device depending on the integral action of the PID controller under stationary conditions; and determining the actual number of revolutions with which to operate the pumping device by means of the sum of the nominal number (N NOM) of revolutions, of the closed-loop contribution (N CL) of the number of revolutions with which to operate the pumping device and of the further contribution (N ADAT) of the number of revolutions with which to operate the pumping device.