This article describes a Bayesian-based method for solving curve fitting problems. We extend the basic linear regression model by adding an extra linear term and incorporating the Bayesian learning. The additional linear term offsets the localized behavior induced by basis functions, while the Bayesian approach effectively reduces overfitting. Difficult benchmark dataset from NIST and high-energy physics experiments have been tested with satisfactory results. It is intriguing to notice that curve fitting, a type of traditional numerical analysis problem, can be treated as an adaptive computational problem under the Bayesian probabilistic framework.