Nowadays, people from every part of the world use social media and social networks to express their feelings toward different topics and aspects. One of the trendiest social media is Twitter, which is a microblogging website that provides a platform for its users to share their views and feelings about products, services, events, etc., in public. Which makes Twitter one of the most valuable sources for collecting and analyzing data by researchers and developers to reveal people sentiment about different topics and services, such as products of commercial companies, services, well-known people such as politicians and athletes, through classifying those sentiments into positive and negative. Classification of people sentiment could be automated through using machine learning algorithms and could be enhanced through using appropriate feature selection methods. We collected most recent tweets about (Amazon, Trump, Chelsea FC, CR7) using Twitter-Application Programming Interface and assigned sentiment score using lexicon rule-based approach, then proposed a machine learning model to improve classification accuracy through using hybrid feature selection method, namely, filter-based feature selection method Chi-square (Chi-2) plus wrapper-based binary coordinate ascent (Chi-2 + BCA) to select optimal subset of features from term frequency-inverse document frequency (TF-IDF) generated features for classification through support vector machine (SVM), and Bag of words generated features for logistic regression (LR) classifiers using different n-gram ranges. After comparing the hybrid (Chi-2+BCA) method with (Chi-2) selected features, and also with the classifiers without feature subset selection, results show that the hybrid feature selection method increases classification accuracy in all cases. The maximum attained accuracy with LR is 86.55% using (1 + 2 + 3-g) range, with SVM is 85.575% using the unigram range, both in the CR7 dataset.