Smoothing splines are well known to be the ideal functions for fitting of discrete data, and also the effective method for smoothing noisy data. Therefore, it is very important to study the construction and computation of smoothing splines. In this paper, the construction and computation of smoothing splines associated with general linear differential operators and linear functionals were discussed. By constructing an appropriate reproducing kernel Hilbert space framework, the proposed splines were expressed as minimum norm problems. Thus the expression and interpolation error of the smoothing spline were obtained via reproducing kernel. Based on this, a new method for computing polynomial smoothing splines was presented.