The model-sequence calculations by the writers of early solar evolution have been extended to the case of a varying-G cosmology. In the varying-G sun there is less lithium depletion than in a constant-G sun, and the time required to burn out central hydrogen is decreased by less than the ratio of luminosities, owing to the much greater total helium production in the varying-G sun. At the present time the varying-G model has four times the 8B neutrino flux of the constant-G model, a prediction that can be subjected to an experimental check.