In order to study the problem of short-term traffic prediction more effectively, experts and scholars have put forward various car-following models. Among data-driven algorithms, k-nearest neighbor algorithm is the most widely used due to its simplicity, flexibility and high accuracy. In this paper, the three-dimensional model based on improved knn algorithm is constructed. It transforms the input vector of basic knn algorithm into a three-row matrix. Data of three dimensions are considered, including only the previous moment data, short period of history data and long period of history data. Three-dimensional matrixes are constructed for prediction and similarity is measured by sum of 2-norm of 3 row vectors. Besides, weighted distance calculation method based on temporal distance is introduced to differentiate impacts data of different dimensions have on the results. Furthermore, time ranges of three dimensions of the input matrix are expanded (including the data of the past 1, 5, and 10 moments respectively). Results show that the model with larger time ranges performs better with 1~5 percentages lower three error evaluation indicators. After experimenting on a single vehicle, this paper examines the prediction results of a group of vehicles following a vehicle using basic kNN model and the three-dimensional one. By comparison, the proposed three-dimensional model reduces prediction error evidently and keeps the mean absolute percentage error under 20% instead of 30% of basic kNN model for most vehicles. In the end, model considering both the preceding car as well as the following car is examined to discover whether taking more cars into account leads to better performance. The results are discussed and analysis is drawn that model considering less vehicles has a slight advantage of reducing prediction error by less than 5% for most vehicles over the other one due to existing redundancy.