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Network robustness is critical for various societal and industrial networks again malicious attacks. In particular, connectivity robustness and controllability robustness reflect how well a networked system can maintain its connectedness and controllability against destructive attacks, which can be quantified by a sequence of values that record the remaining connectivity and controllability of the network after a sequence of node- or edge-removal attacks. Traditionally, robustness is determined by attack simulations, which are computationally very time-consuming or even practically infeasible. In this paper, an improved method for network robustness prediction is developed based on learning feature representation using convolutional neural network (LFR-CNN). In this scheme, higher-dimensional network data are compressed to lower-dimensional representations, and then passed to a CNN to perform robustness prediction. Extensive experimental studies on both synthetic and real-world networks, both directed and undirected, demonstrate that 1) the proposed LFR-CNN performs better than other two state-of-the-art prediction methods, with significantly lower prediction errors; 2) LFR-CNN is insensitive to the variation of the network size, which significantly extends its applicability; 3) although LFR-CNN needs more time to perform feature learning, it can achieve accurate prediction faster than attack simulations; 4) LFR-CNN not only can accurately predict network robustness, but also provides a good indicator for connectivity robustness, better than the classical spectral measures.