Ordinal logistic regression is a statistical method used to analyze the ordinal response variable with three or more categories and predictor variables that are categorical or continuous. The use of ordinal response variables is common in scientific research. We develop an extension of the bivariate ordinal logistic regression model with two correlated response variables in which the relationship between the continuous predictor variable and its logit is modeled as a polynomial form, so it is called the Bivariate Polynomial Ordinal Logistic Regression (BPOLR) model. The aims of this study are determine parameter estimators of the BPOLR model using the Maximum Likelihood Estimation (MLE) method and obtain algorithms of estimating parameters of the BPOLR model. Based on the first partial derivatives, the results are not closed-form. Therefore, it is needed a numerical optimization to obtain the maximum likelihood estimator, namely the Berndt-Hall-Hall-Hausman (BHHH) method.