A wedge-shaped structure made of split-ring resonators (SRR) and wires is numerically simulated to evaluate its refraction behavior. Four frequency bands, namely, the stop band, left-handed band, ultralow-index band, and positive-index band, are distinguished according to the refracted field distributions. Negative phase velocity inside the wedge is demonstrated in the left-handed band and the Snell's Law is conformed in terms of its refraction behaviors in different frequency bands. Our results confirmed that negative index of refraction indeed exists in such a composite metamaterial and also provided a convincing support to the results of previous Snell's Law experiments.