An accurate road surface friction forecasting algorithm can allow travelers and managers to schedule trips and maintenance activities based on the road weather condition to enhance traffic safety and efficiency in advance. Previously, scholars developed multiple forecasting models to predict road surface conditions using historical data. However, historical dataset used for model training may have missing values caused by multiple issues, e.g. the data collected by on-vehicle sensors may be influenced when vehicles cannot travel due to high economic and labor cost or weather-related issues. The missing values in the road surface condition dataset can damage the effectiveness and accuracy of the existing prediction methods. This study proposed a road surface friction forecasting algorithm by employing a time-aware Gated Recurrent Unit (GRU-D) networks that integrate a decay mechanism as extra gates of the GRU to handle the missing values and forecast the road surface friction in future periods simultaneously. The evaluation results present that the proposed GRU-D networks outperform all selected baseline algorithms. The impacts of missing rate on predictive accuracy, learning efficiency, and learned decay rates are investigated as well. The findings can help improve the forecasting accuracy and efficiency of road surface friction prediction using historical data with missing values, therefore mitigating the negative impact of wet or icy road conditions on traffic safety and efficiency.