High dimensional data streams emerge ubiquitously in many real-world applications such as network monitoring. Clustering such data streams differs from traditional data clustering algorithm where the given datasets are generally static and can be read and processed repeatedly, thus facing more challenges due to having to satisfy such constraints as bounded memory, single-pass, real-time response and concept-drift detection. Recently many methods of such type have been proposed. However, when dealing with high dimensional data, they often result in high computational cost and poor performance due to the curse of dimensionality. To address the above problem, in this paper we present a new clustering algorithm for data streams, called RPFART, by combining the random projection method with the adaptive resonance theory (ART) model that has linear computational complexity, uses a single parameter, i.e., the vigilance parameter to identify data clusters, and is robust to modest parameters setting. To gain insights into the performance improvement obtained by our algorithm, we analyze and identify the major influence of random projection on ART. Although our method is embarrassingly simple just by incorporating the random projection into ART, the experimental results on variety of benchmark datasets indicate that our method can still achieve comparable or even better performance than RPGStream algorithm even if the raw dimension is compressed up to 10% of the original one. For ACT1 dataset, its dimension is reduced from 67500 to 6750.