In data mining, classification is a form of data analysis that can be used to extract models describing important data classes. Two of the well known algorithms used in data mining classification are Backpropagation Neural Network (BNN) and Naïve Bayesian (NB). This paper investigates the performance of these two classification methods using the Car Evaluation dataset. Two models were built for both algorithms and the results were compared. Our experimental results indicated that the BNN classifier yield higher accuracy as compared to the NB classifier but it is less efficient because it is time-consuming and difficult to analyze due to its black-box implementation.