According to Hilbert-Huang Transform (HHT) theory, the signals Intrinsic Mode Function (IMF) is extracted by Empirical Mode Decomposition (EMD). Its time-frequency-amplitude spectrum and marginal spectrum are obtained by Hilbert transform. In the basis of summarizing the limitation of the Hilbert transform theory and its realization, an algorithm based on zero-crossing and extremum estimation to obtain instantaneous frequency and instantaneous amplitude is presented. The positions of zero-crossings and extrema are obtained accurately by interpolating the discrete signal. The instantaneous frequency and instantaneous amplitude of relative points are obtained. The signals instantaneous frequency and instantaneous amplitude waveform are obtained by cubic spline interpolation computation. By testing the result and comparing the detail of result with Hilbert transform method through several representative examples, it shows that the instantaneous frequency and instantaneous amplitude obtained by zero-crossing and extremum estimation algorithm are more precise and the frequency resolution is better.