The molecular relaxation of the dynamically asymmetric miscible polymer blend poly(styrene-co-acrylonitrile) (SAN)/poly(epsilon-caprolactone) (PCL) was investigated by differential scanning calorimetry, broadband dielectric spectroscopy, and rheological measurements. The relaxation times and the broadness of relaxation spectrum at both segmental scale and chain scale increase when the temperature decreases. The relaxation times at two length scales are linearly correlated, and the broadness of the terminal relaxation is wider than that of the segmental relaxation. Moreover, it is found that both the segmental relaxation time and the terminal relaxation time increase with the content of the counterpart at the same temperature distance from the effective glass transition temperature. It implies that segmental relaxation time at the effective glass transition temperature is composition-dependent due to the specific interactions between PCL and SAN. By combining the time-dependent diffusion double reptation (TDD-DR) model and the self-concentration and concentration-fluctuation (SCCF) model with the composition-dependent segmental relaxation time at the effective glass transition temperature, the linear viscoelasticity of SAN/PCL blends can be well predicted over a wide range of compositions and temperatures.