Emerging nano-devices with the corresponding nano-architectures are expected to supplement or even replace conventional lithography-based CMOS integrated circuits, while, they are also facing the serious challenge of high defect rates. In this paper, a new weighted coverage is defined as one of the most important evaluation criteria of various defect- tolerance logic mapping algorithms for nanoelectronic crossbar architectures functional design. This new criterion is proved by experiments that it can calculate the number of crossbar modules required by the given logic function more accurately than the previous one presented by Yellambalase et al. Based on the new criterion, a new effective mapping algorithm based on genetic algorithm (GA) is proposed. Compared with the state-of-the-art greedy mapping algorithm, the proposed algorithm shows pretty good effectiveness and robustness in experiments on testing problems of various scales and defect rates, and superior performances are observed on problems of large scales and high defect rates. Emerging nano-devices with the corresponding nano-architectures are expected to supplement or even replace conventional lithography-based CMOS integrated circuits, while, they are facing the serious challenge of high defect rates. In this paper, a new weighted coverage is defined as one of the most important evaluation criteria of various defect-tolerance logic mapping algorithms for nanoelectronic crossbar architectures functional design. This new criterion is proven by experiments that it can calculate the number of crossbar modules required by the given logic function more accurately than the previous one presented by Yellambalase et al. Based on the new criterion, a new effective mapping algorithm based on genetic algorithm (GA) is proposed. Compared with the state-of-the-art greedy mapping algorithm, the proposed algorithm shows pretty good effectiveness and robustness in experiments on testing problems of various scales and defect rates, and superior performances are observ ed on problems of large scales and high defect rates.