In this work, the circular dichroisms (CD) of nanorice heterodimers consisting of two parallel arranged nanorices with the same size but different materials are investigated theoretically. Symmetry-breaking is introduced by using different materials and oblique incidence to achieve strong CD at the vicinity of Fano resonance peaks. We demonstrate that all Au-Ag heterodimers exhibit multipolar Fano resonances and strong CD effect. A simple quantitative analysis shows that the structure with larger Fano asymmetry factor has stronger CD. The intensity and peak positions of the CD effect can be flexibly tuned in a large range by changing particle size, shape, the inter-particle distance and surroundings. Furthermore, CD spectra exhibit high sensitivity to ambient medium in visible and near infrared regions. Our results here are beneficial for the design and application of high sensitive CD sensors and other related fields.