The ocean wave acceleration signal measured from the data buoy system is a key to derive wave features. It is well- recognized that most of the geophysical quantities are usually non-stationary, so are wave acceleration signals. This study applies a method, based on the theory of the continuous wavelet transform and its inverse, to derive the ocean wave scalogram and sea surface elevation from wave acceleration signals. Irregular wave signals are used to verify the practicality of the wavelet algorithm. After analyzing the natural wave acceleration signals, the wave scalogram presents instant wave nonlinearities at some short-time duration from the wave time series records.