<em>This paper presents a proposed supervised classification technique namely flexible partial histogram Bayes (fPHBayes) learning algorithm. In our previous work, partial histogram Bayes (PHBayes) learning algorithm showed some advantages in the aspects of speed and accuracy in classification tasks. However, its accuracy declines when dealing with small number of instances or when the class feature distributes in wide area. In this work, the proposed fPHBayes solves these limitations in order to increase the classification accuracy. fPHBayes was analyzed and compared with PHBayes and other standard learning algorithms like first nearest neighbor, nearest subclass mean, nearest class mean, naive Bayes and Gaussian mixture model classifier. The experiments were performed using both real data and synthetic data considering different number of instances and different variances of Gaussians. The results showed that fPHBayes is more accurate and flexible to deal with different number of instances and different variances of Gaussians as compared to PHBayes.</em>