Support vector regression (SVR) is devised to solve the regression problem by utilizing the excellent predictive power of Support Vector Machine. In particular, the є-insensitive loss function, which is a loss function often used in SVR, is a function thatdoes not generate penalties if the difference between the actual value and the estimated regression curve is within є. In most studies, the є-insensitive loss function is used symmetrically, and it is of interest to determine the value of є. In SVQR (Support Vector Quantile Regression), the asymmetry of the width of є and the slope of the penalty was controlled using the parameter p. However, the slope of the penalty is fixed according to the p value that determines the asymmetry of є. In this study, a new ε-insensitive loss function with p1 and p2 parameters was proposed. A new asymmetric SVR called GSVQR (Generalized Support Vector Quantile Regression) based on the new ε-insensitive loss function can control the asymmetry of the width of є and the slope of the penalty using the parameters p1 and p2 , respectively. Moreover, the figures show that the asymmetry of the width of є and the slope of the penalty is controlled. Finally, through an experiment on a function, the accuracy of the existing symmetric Soft Margin, asymmetric SVQR, and asymmetric GSVQR was examined, and the characteristics of each were shown through figures.