Obtaining soluble proteins in sufficient concentrations is a major obstacle in various experimental studies. How to predict the propensity of targets in large-scale proteomics projects to be soluble is a significant but not fairly resolved scientific problem. Chaos game representation (CGR) can investigate the patterns hiding in protein sequences, and can visually reveal previously unknown structure. Fractal dimensions are good tools to measure sizes of complex, highly irregular geometric objects. In this paper, we convert each protein sequence into a high-dimensional vector by CGR algorithm and fractal dimension, and then predict protein solubility by these fractal features together with Chou's pseudo amino acid composition features and support vector machine (SVM). We extract and study six groups of features computed directly from the primary sequence, and each group is evaluated by the 10-fold cross-validation test. As the results of comparisons, the group of 445-dimensional vector gets the best results, the average accuracy is 0.8741 and average MCC is 0.7358. The resulting predictor is also compared with existing methods and shows significant improvement.