In order to estimate instantaneous frequency (IF), this study proposes a method based on the nonlinear squeezing time–frequency transform (NSTFT). By applying the NSTFT, the method yields a time-frequency (TF) distribution that is a function only of the phase of the input signal. Following this, the algorithm detects ridges to estimate the IF. In the ridge detection algorithm, a second-order smoothing ridge detection algorithm is innovatively proposed by introducing a second-order smoothing term in its cost function. And the various weight factors in the cost function are adjusted according to the local energy condition of the signal. The method can estimate the IF of the signal more accurately in a low signal-to-noise ratio (SNR) case. The normalized mean squared error (NMSE) value of 0.03 can be achieved at a SNR of -10 dB.