This paper deals with L1-norm estimators for nonparametric regression models,where the unknown regression functions are approximated by using B-spline functions.With a potential use of the generalized Akaike information criterion (GAIC) a stepwise forward/backward strategy of selecting the B-spline knots is proposed. A procedure for calculating the L1-norm estimators is presellted via the linear programming technique. The numerical performance of the proposed estimator is compared with that of smoothing spline estimators (SSE) and TURBO based on a simulation experiment. The simulation results indicate that when error distribution is normal or of double exponential power,TURBO, SSE and L1 estimator behave similarly. However, when error distribution is contaminated normal, the performance of L1 estimator is superior to that of TURBO and SSE. When the spline knots are deterministically given, the large sample properties of the L1-norm estimator are discussed.