The disposal of waste tire rubber has gained more attention from the viewpoint of green, environmental protection, and sustainability. Numerous attempts have been stated on the properties of crumb rubber concrete (CRC) and observed that there is a large reduction of compressive strength and elastic modulus of CRC with the increase of the rubber substitution rate. Based on the CRC with the crumb rubber volume content of 5%, the steel fibers and nanosilica were added to CRC to make steel fiber-and-nanosilica-reinforced crumb rubber concrete (SFNS-CRC) in this paper. The effects of the steel fiber volume content and nanosilica content on the compressive properties of SFNS-CRC were studied, including compressive strength, elastic modulus, peak strain, compression toughness, and failure pattern. The test results indicated that the modulus of elasticity and compressive strength of SFNS-CRC have the increasing tendency with the addition of steel fibers and nanosilica. Moreover, the peak strains have a significant increase with the increase of the steel fiber content and nanosilica replacement ratio. The compressive stress-strain curves of SFNS-CRC gradually plump with the increase of the steel fibers and nanosilica. Finally, the prediction formulas for the compressive strength, elastic modulus, and peak strain of SFNS-CRC were set up. A simple predicted model of the stress-strain curve for SFNS-CRC was proposed, which considers the effect of steel fibers and nanosilica.