The full-waveform satellite laser altimeter is able to record the complete backscattered echo waveform from the target surface, which can be used for range measurement and geophysical parameters inversion of the target surface. Some received raw full waveforms of the GF-7 satellite laser altimeter contain significant noise, skewed wave peak, and unsaturated flat peak, causing interferences to the information extraction from waveform. Firstly, an iterative method for waveform background noise removal was proposed, then, the characteristics and geometric structure of the waveform noise were analyzed and quantitatively described, and finally, an adaptive Gaussian filter considering the noise and heterogeneity structure of the waveform was designed. Comparison between the proposed method and other existing classical filtering methods was made in the experiment, and the superior performance of proposed method was proved in noise removal, signal retention, and unsaturated flat peak waveform processing. The higher signal-to-noise ratio (SNR) of the filtered waveform was achieved using the proposed method, and the amplitude decline of the waveform is within 3 times of the noise standard deviation. After the filtering of the waveform with unsaturated flat peak, the decomposition precision of the waveform Gaussian parameter amplitude, mean value and standard deviation are (0.69 ± 2.34) mV, (0.007 ± 0.024) ns and (0.026 ± 0.069) ns respectively.