While the network anomaly detection is essential in network operations and management, it becomes further challenging to perform the first line of detection against the exponentially increasing volume of network traffic. In this work, we develop a technique for the first line of online anomaly detection with two important considerations: (i) availability of traffic attributes during the monitoring time, and (ii) computational scalability for streaming data. The presented learning technique is lightweight and highly scalable with the beauty of approximation based on the grid partitioning of the given dimensional space. With the public traffic traces of KDD Cup 1999 and NSL-KDD, we show that our technique yields 98.5% and 83% of detection accuracy, respectively, only with a couple of readily available traffic attributes that can be obtained without the help of post-processing. The results are at least comparable with the classical learning methods including decision tree and random forest, with approximately two orders of magnitude faster learning performance.