The kinetics of coal/char oxyfuel combustion by isothermal and non-isothermal thermogravimetric analysis is still controversial. The two methods were compared according to the kinetics of two coal chars (NCP anthracite, DT bituminous) combustion in kinetics-controlled regime I under different O-2/CO2 and O-2/N-2 atmospheres. We have developed a surface activation function (SAF, F(X)) to describe the reactive specific surface area of char conversion, and then the intrinsic reaction rate can be expressed by R(X) = kP(O2)(m) F(X), the autocatalysis model (ACM) of F(X) = X-a(1 - X)(c) was found to be suitable under both isothermal and non-isothermal conditions, however, the exponents a and c in ACM as well as the activation energies (E) differ under these two conditions. These controversial results may be caused by the exponential function exp(-E/RT), which changes with the conversion ratio under non-isothermal conditions, which in turn affects the nonlinear modeling results of SAF. According to the isothermal study, temperature has no effect on the form of SAF in Regime I. Thus it is reasonable to use the intrinsic SAF obtained from isothermal experiments (F(X)(iso)) to fit the non-isothermal data. The modeled results show that E-NCP = 207-220 kJ/mol under different O-2/CO2 and O-2/N-2 atmospheres, greater than those under isothermal conditions (178-179 kJ/mol). While E-DT = 159-165 kJ/mol, this agrees well with the isothermal result (163-167 kJ/mol). Furthermore, it indicates that the O-2 partial pressure (P-O2) has no influence on E, even though increasing P-O2 or replacing CO2 in the O-2/CO2 mixture with N-2 increases the intrinsic reaction rate.