Collisions during airport surface operations can create risk of injury to passengers, crew or airport personnel and damage to aircraft and ground equipment. A machine learning model that is able to predict the trajectories of ground objects can help to diminish the occurrences of such collision events. In this paper, we pursue this objective by building a spatial-temporal graph convolutional neural network (STG-CNN) model to predict the movement of objects/vehicles on the airport surface. The methodology adopted in this paper consists of three steps: (1) Raw data processing: leverage Apache Spark to parse a large volume of raw data in Flight Information Exchange Model (FIXM) format streamed from the Surface Movement Event Service (SMES) for the purpose of deriving historical trajectory associated with each object on the ground; (2.1) Graph-based representations of ground object movements: build graph-based representations to characterize the movements of ground objects over time, where graph edges are used capture the spatial relationships of ground objects with each other explicitly; (2.2) Trajectory forecasts of all ground objects: combine STG-CNN with Time-Extrapolator Convolution Neural Network (TXP-CNN) to forecast the future trajectories of all the ground objects as a whole; and (3) Separation distance-based safety assessment: define a probabilistic separation distance-based metric to assess the safety of airport surface movements. The performance of the developed model for trajectory prediction of ground objects is validated at two airports with varying scales: Hartsfield-Jackson Atlanta International Airport and LaGuardia airport, under two different scenarios (peak hour and off-peak hour). Two quantitative performance metrics — Average Displacement Error (ADE) and Final Displacement Error (FDE) are used to compare the prediction performance of the proposed model with an alternative method. The computational results indicate that the developed method has an ADE within the range [7.55, 9.33], and it significantly outperforms an alternative approach that combines a STG-CNN with Convolutional Long Short-Term Memory (ConvLSTM) neural network with an ADE of [15.79, 16.89] in airport surface movement prediction, thus facilitating more accurate safety assessment during airport surface operations.