A score based likelihood ratio (LR) from biometric system plays an important role in forensic science during the determination on how the crime scene evidence is related to a suspect. Traditional methods include logistic regression and kernel density estimation, always neglect the influence of covariates, and embed a large variance of the LR based on our former research. In this paper, we offer a new idea that consider covariates in LR estimation to improve the accuracy of the result. The LR is derived from covariate-specific Receiver Operating Characteristic (ROC) curve with regression estimation, and an order constraint is also adopted for dealing with the stochastically ordering property. This property is naturally arising for the biomarkers and devices. We also introduce a new method to estimate the order constraint regression coefficient in a short amount of time.