Fixed censorship is usually encountered in medical fields, as well as biological, econometric, and engineering researches. It is quite possible to come across censored data with multicollinearity in real-life studies. The multicollinearity affects traditional Tobit maximum likelihood estimation, which is often used in presence of censored data. Biased estimators such as Tobit Liu estimator with one biasing parameter can be used for solving the multicollinearity. In this study, Tobit two-parameter estimator with two biasing parameters is proposed as an alternative to the classical Tobit maximum likelihood and Tobit Liu estimators for the censored data. This new estimator provides advantages from two different aspects thanks to having two biasing parameters. With a simulation study consisting of several scenarios where various levels of factors like the number of independent variables, sample size, correlation degree, variance, and censorship are examined, an in-depth experimental analysis is conducted. In these scenarios, two different biasing parameters' selection methods where one of the biasing parameters is fixed to determine the other one are used and their corresponding outputs are obtained. In addition, a real-life application is carried out with the National Health and Nutrition Examination Survey public-use dataset which includes some demographic and health-related laboratory measurements. The simulation study and data analysis results show that the proposed estimator is more advantageous to its competitors.