The popularity of Twitter as a social media platform is increasingly becoming very important, this has no doubt impact positively on the business, social and political aspect of our lives, and hence, the need for researchers to focus on Twitter opinion miming became crucial. Despite the increase in the number of Twitter users in Nigeria generating a huge amount of data from the discussions on national issues became a challenge; limited research has been carried out on Twitter data sources from Nigerian context. The objective of this paper is to use Twitter data from Nigeria to carry out a comparative analysis of the performance criteria based on accuracy, precision and recall on three classification algorithms. The purpose of which is to find out the best algorithm that fits the dataset. Dataset used was gathered using Twitter Application Programming Interface (API) given a trending hash tag on national issues. This dataset was preprocessed before modeling. Twitter opinion mining classification algorithms: Naïve Bayse, Support Vector Machine (SVM) and Maximum Entropy were chosen, modeled and evaluated. Findings from this research show that dataset from Nigeria can be used to mine the opinions of citizens on national issues; it also shows that SVM was disappointing using the dataset, while Naïve Bayse classifier outperform others with accuracy of 83%; this is implying that the best among the three models can classify tweets wrongly with the rate of 17%. The best model (Naïve Bayse) was implemented as Software; the Software downloads and automatically classifies tweets into three opinions namely positive, negative and neutral.