Bayesian identification has attracted considerable interest in various research areas for the determination of the mathematical model with suitable complexity based on input-output measurements. Regression analysis is an important tool in which Bayesian inference and Bayesian model selection have been applied. However, it has been noted that there is a subjectivity problem of model selection results due to the assignment of the prior distribution of the regression coefficients. Since regression coefficients are not physical parameters, assignment of their prior distribution is nontrivial. To resolve this problem, we propose a novel nonparametric regression method using Bayesian model selection in conjunction with general regression. In order to achieve this goal, we also reformulate the general regression under the Bayesian framework. There are two attractive features of the proposed method. First, it eliminates the subjectivity of model selection results due to the prior distribution of the regression coefficients. Second, the number of model candidates is drastically reduced, compared with traditional regression using the same number of design/input variables. Therefore, this allows for the consideration of a much larger number of potential design variables. The proposed method will be assessed and validated through two simulated examples and two real applications.