Statistics is the science that aims to collect and analyze data. In data analysis, researchers need to collect all information that serves their study. Using full information about the parameter leads to fitting an appropriate model for the data that researchers collect. This study aimed to fit a constrained beta regression model using prior information (BCML). Mean square error (MSE) has been used to justify the new estimator. Real data and simulation have been done using R.4.2.2. Results indicate that the constrained beta regression is better than the standard beta regression, where its MSE was less.