In this work, we investigate the effectiveness of a novel fractal feature-based technique in predicting glaucomatous progression using the retinal nerve fiber layer (RNFL) thickness measurement data. The technique is used to analyze GDx variable corneal compensator (GDx-VCC) scanning laser polarimeter (SLP) data from one eye of 96 study participants (14 progressors, 45 non-progressors, and 37 ocular normal patients). The novel feature is obtained by using a 2D box-counting (BC) method, which utilizes pseudo 2D images from 1D temporal, superior, nasal, inferior, temporal (TSNIT) RNFL data. For statistical performance evaluation and comparison, we compute sensitivity, specificity and area under receiver operating curve (AUROC) for fractal analysis (FA) and other existing feature-based techniques such as fast Fourier analysis (FFA) and wavelet-Fourier analysis (WFA). The AUROCs indicating discrimination between progressors and non-progressors using the classifiers with the selected FA, WFA, and FFA features are 0.82, 0.78 and 0.82 respectively for 6 months prior to progression and 0.63, 0.69 and 0.73 respectively 18 months prior to progression. We then use the same classifiers to compute specificity in ocular normal patients. The corresponding specificities for ocular normal patients are 0.86, 0.76 and 0.86 for FFA, WFA and FA methods, respectively.