To assess the mutational robustness of nucleic acids, many genome- and protein-level studies have been performed; in these investigations, nucleic acids are treated as genetic information carriers and transferrers. However, the molecular mechanism through which mutations alter the structural, dynamic and functional properties of nucleic acids is poorly understood. Here, we performed SELEX in silico study to investigate the fitness distribution of the nucleic acid genotype neighborhood in a sequence space for L-Arm binding aptamer. Although most mutants of the L-Arm-binding aptamer failed to retain their ligand-binding ability, two novel functional genotype neighborhoods were isolated by SELEX in silico and experimentally verified to have similar binding affinity (Kd = 69.3 μM and 110.7 μM) as the wild-type aptamer (Kd = 114.4 μM). Based on data from the current study and previous research, mutational robustness is strongly influenced by the local base environment and ligand-binding mode, whereas bases distant from the binding pocket provide potential evolutionary pathways to approach global fitness maximum. Our work provides an example of successful application of SELEX in silico to optimize an aptamer and demonstrates the strong sensitivity of mutational robustness to the site of genetic variation.