Magnetic reconnection is studied based on a two-dimensional magneto-hydrodynamic simulation model. We observe in our simulation study both the magnetic reconnection with a fast mode expansion (Pletschek model) and the reconnection with a slow mode expansion (Sonnerup-Yeh-Axford model) upstream of the field reversal region. It is found that the slow mode expansion tends to occur when the system length is long, the imposed reconnection rate is high, or the resistivity is large. On the other hand, the fast mode expansion becomes dominant for a system with a short length, a low reconnection rate, or a small resistivity.