Semi-parametric models are often used to fit data collected in receiver operating characteristic (ROC) experiments to obtain a smooth ROC curve and ROC parameters for statistical inference purposes. The proper bibeta model as recently proposed by Mossman and Peng enjoys several theoretical properties. In addition to having explicit density functions for the latent decision variable and an explicit functional form of the ROC curve, the two parameter bibeta model also has simple closed-form expressions for true-positive fraction (TPF), false-positive fraction (FPF), and the area under the ROC curve (AUC). In this work, we developed a computational algorithm and R package implementing this model for ROC curve fitting. Our algorithm can deal with any ordinal data (categorical or continuous). To improve accuracy, efficiency, and reliability of our software, we adopted several strategies in our computational algorithm including: (1) the LABROC4 categorization to obtain the true maximum likelihood estimation of the ROC parameters; (2) a principled approach to initializing parameters; (3) analytical first-order and second-order derivatives of the likelihood function; (4) an efficient optimization procedure (the L-BFGS algorithm in the R package “nlopt”); and (5) an analytical delta method to estimate the variance of the AUC. We evaluated the performance of our software with intensive simulation studies and compared with the conventional binormal and the proper binormal-likelihood-ratio models developed at the University of Chicago. Our simulation results indicate that our software is highly accurate, efficient, and reliable.