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Alkali-metal atomic magnetometers employing longitudinal carrier magnetic field have ultrahigh sensitivity to mea-sure transverse magnetic fields and have been applied in a variety of precise-measurement science and technologies.In practice,the magnetometer response is not rigorously proportional to the measured transverse magnetic fields and the exist-ing fundamental analytical model of this magnetometer is effective only when the amplitudes of the measured fields are very small.In this paper,we present a modified analytical model to characterize the practical performance of the magnetome-ter more definitely.We find out how the longitudinal magnetization of the alkali metal atoms vary with larger transverse fields.The linear-response capacity of the magnetometer is determined by these factors:the amplitude and frequency of the longitudinal carrier field,longitudinal and transverse spin relaxation time of the alkali spins and rotation frequency of the transverse fields.We give a detailed and rigorous theoretical derivation by using the perturbation-iteration method and simulation experiments are conducted to verify the validity and correctness of the proposed modified model.This model can be helpful for measuring larger fields more accurately and configuring a desirable magnetometer with proper linear range.