Grapevine is one of the most economically important fruit crops cultivated worldwide. However, grapevine is highly susceptible to virus infections and exposed to the most diverse forms of viral diseases compared to other fruit crops, and virus-induced incompatibility affects plant growth to different degrees ranging from decline to death. The influence of virus-induced incompatibility could be mitigated to an acceptable level by using appropriate rootstocks. However, the viral tolerance of various grapevine rootstocks with diverse genetic backgrounds remains unclear, along with the identification of the specific viral tolerance factors. In this study, the viral tolerance of 21 grapevine rootstocks was evaluated in a green grafting system. Cabernet Franc varieties infected with a single virus [grapevine leafroll associated virus-1 (GLRaV-1)], a co-infection of two viruses (GLRaV-1 plus grapevine virus A—GVA), and no infection were used as the scions, respectively. The vegetative growth and photosynthetic function of the grafts were analyzed 4 months after grafting. The results indicated that some rootstocks could alleviate the influence of the virus infection, with vegetative growth and photosynthetic function sustained at a normal level, whereas other rootstocks were susceptible to the virus infection, resulting in a decline in the growth and photosynthetic function of the grafts. Our research provides evidence for the existence and diversity of viral tolerance among grapevine rootstocks, offering important information for appropriate rootstock selection in the establishment of new vineyards and in the breeding of grapevine rootstocks with enhanced viral tolerance.