Noise is an important factor of affecting range error for satellite laser altimeter with recording waveform. According to the distribution characteristic of received pulse signal and noise, the theoretical expression form about variance of time-centroid for received pulse signal was deduced. Thereby, the impact model of noise on range error was built-up. Base on the principle of minimizing range error, an optimization design method for low-pass filter was put forward. In terms of basic measurement parameters for Geoscience Laser Altimeter System(GLAS), the distribution regularities of range error and RMS pulse width for low-pass filter were simulated. As for linear target of geometrical parameters within 40° slope angle and 15 m roughness, the extent of range error is 0.28-32.49 cm. Correspondingly, the scope of RMS pulse width for low-pass filter is 1.4-57.4 ns. Aimed at targets with scope of 1° slope angle, the computed value of low-pass filter for GLAS is 2.2 ns, which is close approximate to 2 ns as published practically value. Meanwhile, on basis of optimizational results for low-pass filter, the range errors decrease significantly. The maximum of range error is decreased to 10.93 cm and corresponding reduction level gets 3 times. All the results show that impact model of noise on range error and optimization design method for low-pass filter is correct. They provide practical application values for hardware design and performance assessment of satellite laser altimeter.