The low-temperature creep compliances (D(t)) of asphalt mixture is one of the necessary parameters to predict the depth and amount of low-temperature cracks. Level 3 analysis in Mechanistic-Empirical Pavement Design Guide (MEPDG) software uses asphalt binder properties parameters and mixture volumetric properties to predict D(t) when the real laboratorial data is not available. However, some parameters in the model may not be routinely measured in Superpave system, which restricts the use of the prediction model. In addition, new additives and recycling materials such as reclaimed asphalt pavement (RAP) have been extensively used in recent years and shown to have significant effect on the low-temperature cracking resistance of asphalt mixture. However, the effects have not been considered in the existing D(t) prediction models. Hence, the objective of this study is to develop models with significantly high accuracy to predict the D(t) of asphalt mixtures containing RAP. A total of 1890 sets of data points were collected from three different research projects. A Pearson correlation analysis was carried out to select the input parameters which are most influential to D(t). Two prediction models (i.e., multiple linear regression and artificial neural network (ANN) models) were proposed. A comprehensive analysis on the prediction accuracy and reasonability of the proposed models was conducted. The results showed that the proposed models had much better prediction performance with high accuracy than the existing models. The comparisons between the proposed models with the existing models confirmed that it is necessary to take the new additives and recycling materials into account in developing D(t) prediction models.