Abstract: Inspired by intuitive meanings of truncated power basis's coefficients, the local penalization based on range's linear decreasing function is given in penalized spline regression model. This method gives less penalization to fitting curve where data is with more volatility, which makes fitted curve controls tradeoff between goodness-of-fit and smoothness better. Simulations show that regression models with local penalized spline obtain lower information rules' scores than global penalized spline when the data is with heteroskedasticity.