The Greenland and Antarctic ice sheets are important indicators of climate change and major contributors to sea level rise. Hence, precise, long-Term observations of ice mass change are required to assess their contribution to sea level rise. Such observations can be achieved through three different methods. They can be achieved directly by measuring regional changes in the Earth's gravity field using the Gravity Recovery and Climate Experiment Follow-On (GRACE-FO) satellite system. Alternatively, they can be achieved indirectly by measuring changes in ice thickness using satellite altimetry or by estimating changes in the mass budget using a combination of regional climate model data and ice discharge across the grounding line, based on multi-sensor satellite radar observations of ice velocity . Satellite radar altimetry has been used to measure elevation change since 1992 through a combination of various missions. In addition to the surface slope and complex topography, it has been shown that one of the most challenging issues concerns spatial and temporal variability in radar pulse penetration into the snowpack. This results in an inaccurate measurement of the true surface elevation and consequently affects surface elevation change (SEC) estimates. To increase the accuracy of surface elevation measurements retrieved by retracking the radar return waveform and thus reduce the uncertainty in the SEC, we developed a deep convolutional-neural-network architecture (AWI-ICENet1). AWI-ICENet1 is trained using a simulated reference data set with 3.8 million waveforms, taking into account different surface slopes, topography, and attenuation. The successfully trained network is finally applied as an AWI-ICENet1 retracker to the full time series of CryoSat-2 Low Resolution Mode (LRM) waveforms over both ice sheets. We compare the AWI-ICENet1-retrieved SEC with estimates from conventional retrackers, including the threshold first-maximum retracker algorithm (TFMRA) and the European Space Agency's (ESA) ICE1 and ICE2 products. Our results show less uncertainty and a great decrease in the effect of time-variable radar penetration, reducing the need for corrections based on its close relationship with backscatter and/or leading-edge width, which are typically used in SEC processing. This technique provides new opportunities to utilize convolutional neural networks in the processing of satellite altimetry data and is thus applicable to historical, recent, and future missions.