Online learning has witnessed an increasing interest over the recent past due to its low computational requirements and its relevance to a broad range of streaming applications. In this brief, we focus on online regularized regression. We propose a novel efficient online regression algorithm, called online normalized least-squares (ONLS). We perform theoretical analysis by comparing the total loss of ONLS against the normalized gradient descent (NGD) algorithm and the best off-line LS predictor. We show, in particular, that ONLS allows for a better bias-variance tradeoff than those state-of-the-art gradient descent-based LS algorithms as well as a better control on the level of shrinkage of the features toward the null. Finally, we conduct an empirical study to illustrate the great performance of ONLS against some state-of-the-art algorithms using real-world data.