In this paper, the author numerically investigates the effect of a staggered arrangement on the vortex-shedding of two circular cylinders with unequal diameters under a subcritical Reynolds number. The results show that the interference between the large and small cylinders was prominent at a positional angle of α=30{degree sign}. The time histories of the lift and drag coefficients exhibited severe anomalous jumps, and the number of dominant shedding frequencies of the vortices shed from the small cylinder was usually two and three. As the gap ratio ( G/ D) became greater than 0.75, the time histories of the lift and drag coefficients at α=60{degree sign}, 120{degree sign}, and 150{degree sign} tended to become stable, with the weakening of the interference between the large and small cylinders. When α=150{degree sign}, the modes of action of flow in the gap for the large and small cylinders were similar under different gap ratios. The Strouhal number of the large cylinder was in the range of 0.18~0.23 overall while that of the small cylinder gradually approached 0.2, with an increase in G/ D when α=60{degree sign}~150{degree sign}.