The non-linear frequency modulation signal is common and significant in signal processing. In order to improve the resolution and energy of its time-frequency representation (TFR), this paper proposed a new time-frequency analysis method known as the Fourier Transform with the adaptive kernel (AK-FT). According to Weierstrass approximation theorem, nonlinearly time-varying frequency can be expressed in weighted exponential function in a continuous time. The nonstationary signal is able to be transferred into the stationary one. The TFR with excellent concentration is produced through the Fourier Transform, and the accuracy of the instantaneous frequency of the non-linear frequency modulation signal is also improved. Compared with the traditional time-frequency analysis, this method can estimate the time-frequency parameters of non-linear frequency modulation signal analysis reliably and precisely.of