This paper introduces a novel framework for fast parameter identification of personalized pharmacokinetic problems. Given one sample observation of a new subject, the framework predicts the parameters of the subject based on prior knowledge from a pharmacokinetic database. The feasibility of this framework was demonstrated by developing a new algorithm based on the Cluster Newton method, namely the constrained Cluster Newton method, where the initial points of the parameters are constrained by the database. The algorithm was tested with the compartmental model of propofol on a database of 59 subjects. The average overall absolute percentage error based on constrained Cluster Newton method is 12.10% with the threshold approach, and 13.42% with the nearest-neighbor approach. The average computation time of one estimation is 13.10 seconds. Using parallel computing, the average computation time is reduced to 1.54 seconds, achieved with 12 parallel workers. The results suggest that the proposed framework can effectively improve the prediction accuracy of the pharmacokinetic parameters with limited observations in comparison to the conventional methods. Computation cost analyses indicate that the proposed framework can take advantage of parallel computing and provide solutions within practical response times, leading to fast and accurate parameter identification of pharmacokinetic problems.