The advancement in Internet of things and sensor technologies has enabled data to be continuously generated with a high rate, i.e., data streams. It is practically infeasible to store streaming data in a hard disk, and apply a traditional batch learning method to extract a relevant knowledge model from these data. This paper studies online incremental learning with data streams, in which one sample is processed at each time to update the existing model. For the learning target, the Bayesian classifier is adopted which is a computationally economical model of easy deployment for online processing in edges or devices. By using the individual new example, we first present an online learning algorithm to incrementally update classifier parameters in a way equivalent to the offline learning counterpart. In order to adapt to concept drifts in nonstationary environments, the proposed online learning algorithm is improved to enable recent examples to be more impactful during the sequential learning procedure. Preliminary simulation tests reveal that the improved online learning algorithm can lead to faster model adaption than the unimproved online algorithm when the data drift occurs. In case of presumed stationary data streams without drifts, the improved online algorithm is proved to be competent by performing at least as good as (sometimes, even better than) the unimproved algorithm.